I doubt it. The Spurs are looking for a veteran who can rebound and play defense. Big Baby only grabs around nine percent of all possible rebounds. He averaged only 5.6 rebounds and .2 blocks. That's one block every five games! I truly believe the only possible way he ends up in San Antonio is if they can sign both him and Drew Gooden, which is highly unlikely.
One more thing is that the Spurs already have a player that plays the exact same style as Big Baby in Dejuan Blair. Blair may even prove to be better at it.
As of right now, the only serious plans I have heard are: Plan A: Sign Antonio McDyess, or plan B: Sign Drew Gooden. Both are higher priority, both are higher caliber and both would more likely end up in San Antonio than Davis. Anything else would be highly unlikely.