I can't see why they wouldn't. With offense around the league as bad as it is, a good lefthanded bat off the bench that can play three positions and get on base at a good clip isn't a bad asset.
It comes down to whether they can trade Cespedes. If they can, I fully expect Nava to be on the bench next year. If not, you've got your 5 outfielders in Cespedes, Betts, Castillo, Victorino, and Hanley and there's no room for Nava except as your putative backup 1B.
There is another option though -- we could trade Mike Napoli. He's a good righthanded power hitter and I'd hate to lose him, but if trading him allows us to put Sandoval at 1B where his limited range hurts us less and his great hands help us more, and Hanley at third, then spaces open up in the outfield for both Cespedes and Nava.