Why He'll Survive
Varys' nickname is the Spider, but he's more like a cockroach when it comes to survival instinct. He is one of the great manipulators of the game, and since his rival conspirator Littlefinger is almost definitely going to die sooner rather than later (Season 7 makes sense), it stands to reason that Varys would continue to live.
Where Varys really differs to Baelish, though, is that he spins his webs and uses his little birds for the good of the realm, not to win power for himself. That means he should be on the winning side, and alive as a result. Also, imagine if almost everyone dies and only a few survive to repopulate Westeros... and one of them is a eunuch. Now that's bittersweet.
Why He Might Not
Again, Varys is another character who won't be much use in a fight, and thus could well be killed off as the Battle of Ice and Fire shapes up.