No, not yet. He's not in Kawhi's situation, because he's not Kawhi.
Giannis does a lot of things well, but he's a .274 three point shooter. Kawhi is a .388 three point shooter, but more importantly, he is the 2-time reigning DPOY, was 1st team all-NBA last year and came in second in MVP voting last season.
If you swapped the players, MIL would definitely get better, and I suspect SAS would get a little worse. Again Giannis does a lot of things well, but so does Kawhi and I think the things Kawhi does better are more vital to the Spurs success (better shooter and much better defender - the best in the league).
BNM