If you rely solely on GPS to cross an ocean, you will not know if you are right until the last day.
With that said, the real answer to the question is: You have a good chance these days of getting by without celestial navigation.
...In fact, you don't even need a boat to get to Hawaii or Bermuda, or to take a trip around the world. You can do this by plane. It is faster, cheaper, and more comfortable, and it will increase your likelihood of not needing celestial navigation as well.
On the other hand, if you do choose a life on a small boat at sea, then one of the fundamental rules that has been proven so many times we don't have to go over it is you must be prepared to take care of yourself in any contingency. You must be self reliant. Murphy's Law was invented on a small boat at sea. Anything electrical is vulnerable after some time in the salt air, especially when it is being jarred, bumped, banged, and dropped (i.e. going to weather).
To be self reliant, we need some dependable means of navigation, and celestial is that. Needless to say, a hand-held GPS and spare batteries stuffed into a well protected vacuum sealed bag is a pretty good back up these days, but it is not at all bullet proof. Batteries of any kind are not bullet proof. One could even argue that the durability of hand held GPS units is not improving at all with time. They are getting cheaper, and have more functions, but no evidence of more dependable.
Furthermore, you are still dependent on the availability of the signals. In any sort of worldwide military conflict, it is likely you would lose these first thing. (Here is a March, 2016 example of US military shutting it off over hundreds of miles.) In principle, you could lose the signals in a union dispute. It doesn't really matter. Or lose them as a result of a "pre-commissioning validation exercise!"
See also question 724 of the USCG Deck License exam questions on GPS.
Keep in mind as well that GPS has always been notoriously easy to jam either maliciously or accidentally, so you could get stuck one day without it. Here is an example from 2011, and here shows our progress as of 2013. Google GPS jamming for more discussion. See also this note from Feb 2014: GPS pioneer warns on network’s security.
See also:
www.bbc.co.uk/news/uk-scotland-highlands-islands-15242835
and
www.techweekeurope.co.uk/workspace/mod-halts-gps-jamming-after-safety-complaints-42074
And here is a database started in 2015 of GPS jamming events.
There are also numerous examples of GPS failures linked in the comments below.
But quite beyond the numerical likelihood of not having it when you need it, still a very small probability, learning celestial is still a most rewarding venture. It will make you a better navigator even on inland and coastal waters—you must, for example learn how to do a running fix to do celestial, and this could well pay off if you lost the GPS for some reason, and were left with just one light shining through the fog; or you are close in on a coast, but can then only identify one feature on the land (which is not a radar target), etc. Such problems are easily solved with a running fix.
In some areas of the world you can have precise GPS coordinates, but no chart scale adequate to navigate on with Lat and Lon. You have to use basic piloting skills. This is not celestial navigation itself, but the question is, if you choose to not learn celestial because of GPS for worldwide navigation, what else are you prepared to not learn?
But back to the celestial. Once you learn celestial, it is a trivial matter then to check your compass with the bearing to some celestial body, even well away from any land marks and in a strong unknown current. You can't do this with GPS in a dependable manner (in current and leeway), nor any other instrumentation on board, no matter what it cost, and no matter if you are a ship or a sailboat. The only way to truly check your compass at sea is with celestial. And if the boom hits your compass or lightning strikes near by, or–much more likely–you simply realize that it never was checked before, then this is something you will eventually have to do.
In the last 4 or 5 ocean crossings I took part in, we did maybe take a sight or two for practice but we did not feel compelled to do celestial for basic navigation, and it was not needed. But, we did use cel nav on each of these voyages to check the compass. Ironically, the more technical the vessels become, the more this need arises. That is, we now have multiple compasses on board with heading sensors for the other electronics, and inevitably they will not agree, and if this does not get sorted out before leaving the dock, you are left to do it underway.
(In passing, the last ocean crossing that I did that relied solely on celestial navigation was in July 1982. And all the details of that navigation is presented in a new book from Starpath called Hawaii by Sextant. It is a thorough and enjoyable way to master the subject of celestial navigation with real sights and real logbook entries. See also this article about that book and an overview of cel nav in general.)
And finally, there is a wonderful intellectual satisfaction that comes from learning and practicing celestial navigation. It is a way to see science and math come together in our own hands and mind and do something both tangible and useful.
Learning celestial will make you a better ocean mariner because whether you show it or not, you will be anxious about your navigation if you are depending on something that we (most of us) cannot hope to understand. GPS is the quintessential black box. With nothing else to check it with, you can just hope and pray that it works right, and, again, you will only really know that on the last day, when you either see the right land or do not. And when you are anxious, you are more likely to make a mistake.... and you risk the chance of exposing your anxiety to the crew, which could undermine your leadership, which in turn could lead to all sorts of unpleasantness. None of that will happen of course so long as everything is going fine, but if things start to get stressed for any reason (bad weather, broken gear), this factor will just add to the challenge.
In the long run, it is best to learn celestial, even if you are never going to use it. You will know you can use it if you need to, and that alone will make it worthwhile. If you plan to crew on other vessels, then knowing celestial will be an important part of your credentials and will certainly help you find a good position. The majority of skippers will believe they do not need it, but they will be happy to know someone on board does know it.
In contrast to GPS, celestial navigation is completely transparent. If you are confident that your watch is right, then you must be located at the intersection of the 3 star lines you have plotted. There is no mistake you can make and still get that confirmation. Likewise, if you make a mistake, it will generally stand out like a sore thumb and you can go back over your work and find the error. With celestial navigation, you are crossing an ocean with the same confidence you would be sailing from headland to headland on inland waters. Think of it as sky piloting.
And one last related thought: GPS is (in an abstract sense) another version of SatNav (the Navy Transit System, now long gone) that happens to be a lot easier to use and is more accurate. But in this sense, we have had all-weather global satellite positioning for more than 30 years now. Yet there never was any consideration at all by the USCG to remove the requirement of learning celestial from an ocean license exam. And there is none now. To get a USCG license that is valid offshore you need to know celestial and pass a test on it. Whatever the reasoning behind that decision for ships, it is many-fold increased for small boats at sea.
Still a required part of professional training.
