Haha, I don't think they do. I wouldn't, provided that I believed in my reasoning above. The Spurs could feel differently, of course. This may be a different story in the off-season, if the Spurs lose Splitter and have cap room lying around. A player like McGee would be helpful them. I just made the argument for trading for McGee because I feel like they could if they wanted to.
I'll say this though: There are things that make it easier for the Spurs to have McGee instead of Splitter and Green that aren't there for the Nuggets:
Wing security: They have Kawhi and De Colo locked up and can re-sign Neal. If Manu and/or Jack come back, there'd be a struggle to find minutes for everyone even minus Green.
Cap prognosis: They don't have as much money committed long-term as the Nuggets do. making that trade doesn't even eat all of San Antonio's cap space, let alone pushes them toward the tax.
Rotation: There's no reason why Duncan would not be able to start with McGee. (We now know he can spread the floor

.) So McGee would probably start for the Spurs. A big reason why the Nuggets would be better is because they'd get Green, who'd allow everyone to slide over to their natural positions. Losing Green doesn't have the same effect for the Spurs.
These may seem like tiny differences, but I do think they're big enough that it's not clear cut that the Spurs and Nuggets would be equally affected by this swap.