The Spurs have entered free agency with zero spots before. Anyways, my point isn't that stashing is wrong or whatever; it's that you can't reliably find guys who are willing to be stashed. There's no reason to select a player who's way worse than who's available just because that player is willing to be stashed. It could work out that someone intriguing is there and is good value. But the team has to prepare for the possibility that they'll need to use the pick. They're not the only team with multiple selections that may not have enough roster spots.
You can't stretch a guy and re-sign him in the same year. You can waive a guy and bring him back. That usually happens with low-level players, like James Anderson back in the day. When that happens, you do have both figures on the books, and those figures operate independently. Like if the Spurs waived Pau and then brought him back on a min deal, they'd have the $7ish Million contract and the $2ish Million contract, and they'd only be able to trade the latter.
I'd be decently surprised. If they don't want the pick, they'll use it before then as part of a trade. In this scenario where SA also has a good second, that'll be the one they'd stash. Or they'd combine those it and the TOR pick rather than worrying about the SA first.
The entire Milutinov situation pisses me off. I do think that they had interest in bringing him over and didn't have interest anymore (at least for this season) after they traded for Poeltl. I can't say if Nikola wanting too much made them covet Poeltl over Siakam or OG (and I would break something if that got confirmed) or if having to settle on Jakob killed any incentive to cave to Milutinov. But I could see him being traded or just let go if they can't work something out. I wouldn't pay more than rookie-scale for him right now, but he can get twice that in Europe just being who he is.