Expansion of the universe and visibility of distant galaxies
(My answer here isn't correct, as pointed out by the first comment on this post, please refer to it.)

Yes, it certainly is possible - and it already has happened. The age of the universe is 13.8 billion years, yet it is something like 90 to 100 billion light-years in diameter. This means that we definitely can't see all of it, not because of our own observational limitations, but because the light from those parts of the universe just hasn't reached us yet - and perhaps it never will.

As for the future, yes, if cosmological expansion overpowers gravity at close range (i.e. the Milky Way and Andromeda, and the world "close" is relative here) then eventually many galaxies and clusters will disappear out of view due to light not being able to "keep up" with the expansion.