Here are a few pictures of the sun taken over a 3 or 4 minute period. Before this it was all grey; after this is was again all grey.
With a standard 4x40 scope with standard sun shade you would be able to get sights of this sun at the times of the best views below, providing you were standing there waiting and ready to go. You might just have a few seconds, but as long as you can see the outline of the disk you can get a sun line. It might not be your best work, but it will be usable if that is all you have.
This is a point that came up several times in the voyage documented in Hawaii by Sextant. At the end here we show that it can't be too far off, even in these cases.
To get a feeling for how far off a sight like this could be, we take a look at the scale of things.
When we take a sun sight, the bottom edge of the sun should just touch the horizon. Our job in all sights is to be sure this is aligned as precise as possible. But how far can we be wrong? The semi-diamter of the sun is about 16'. The sun above is not aligned properly; that is very easy to see. This one is off by 2'. Even half of this would be very easy to see. In short, we should be able to line up the sun in even just reasonable conditions to well within a mile (1' or so). The sun can be very sharp in a scope behind a filter, even when it is very fuzzy or not even discernible without these aids.