My Strat is 1 5/8", which is 41.275 mm, so yes, playable, and some people even like it.
Doesn't really matter whether it's flatpicked or fingerpicked, since that's going on way down by the saddle where the string spacing is wider and not necessarily related to the nut width. The main impact of a narrow nut is going to be on cowboy chords and barred chords up by the nut, making them somewhat easier to play but harder to play cleanly.