I have to agree with Bruno here. Gortat is a good player but he just doesn't fit. Anything Gortat gives you on the boards and on defense will be negated by the fact that he has no offensive game. Gortat survives on the Magic because they literally don't use an interior player when he's in the game more than 90% of the time. But in San Antonio, where each member of the Big 3 is best in the paint, having Gortat as one of the other two players on the court will just cause way too much congestion.
All teams would do is leave Gortat open and pack the lane and the Spurs' offense would stall. The bigman next to Duncan has to have some level of skill to survive. If Gortat had a post game, a jumper, passing ability or anything of note, I'd consider enter the bidding war. But he has no offensive game at all. If you stop him from dunking or laying it up, he's toast.
Defensively, yeah he'd be a very nice addition. Rebounding-wise, he'd make the Spurs an even better rebounding team. But his utter lack of any offensive game would cancel all of that out. You can say Duncan will play the high post but that's not even the biggest issue. The biggest issue is that the opponent's would use Gortat's man to clog up lanes for the Big 3. Teams wouldn't have to respect Duncan's drives, they could much easier shut down the lane on Parker and they could send extra help at Ginobili.
I know it's difficult to turn down a good bigman when the Spurs are currently starting Bonner but Gortat isn't the answer for what he's going to make this summer.