I hope Bobby Marks is right about this, but I find it highly unlikely. Looking at the rosters and the available picks there are very few contenders that'd need an undersized back up center and the ones who could really use him ( Brooklyn, Golden State, Chicago ) don't have the contracts or picks to make a deal work.
That said, I'm not sure the Spurs would value late first round picks as much as us message board folks do. If they have plans for the cap space they might have next summer I don't think they'd blow it on the chance they'll have a 25th pick or something 3 years from now. Like, I'm pretty sure they see more value in McDermott, for example, compared to a late pick.
On the specific trade, I'd do it right away because I don't know of their cap space plans and because I've always liked Saric and think he could actually be an asset.