I looked it up and Kidd's knee started hurting him in the beginning of the 2003-04 season. By the end of the season and the playoffs he could hardly move and he shot something like 33% after Christmas and 25% on three-pointers.
Looking back on it, the Nets thought Kidd's originally hurt his knee during the 2002-03 season. One of the first signs he had lost a step is that he couldn't guard Parker at all in those finals.

He eventually had the microfracture surgery after the 2004 playoffs.
So yeah, if the Spurs the Spurs would have signed Kidd, their first year of a healthy Kidd would have been the 2005-06 season and by then Parker and Ginobili would have been long gone. And probably Duncan as well.