Yes.
Look, the RJ hate is strong here on ST. The Spurs operate more rationally. While many here believe that the Spurs become a better team simply by making RJ disappear, I doubt that the FO holds the same view.
Using the amnesty this year saves some luxury tax and adds the lux tax distribution. The FO may view this as a small price to pay for a player who has some useful skills and can eat minutes during a compressed schedule while a rookie is integrated into the team. The only spending flexibility they gain from using the amnesty is the increase from the mini-MLE to the full MLE.
Using the amnesty next year, in conjunction with a Duncan retirement, creates a substantial amount of cap space.
Keeping him also allows for the possibility of a trade. While it may seem unlikely now, you never now how the season will unfold. A contending team could lose their SF to injury before the trade deadline and may be willing to swap an expiring contract to get a veteran with playoff experience. Once the amnesty is used, all you can do is pay the guy to play for someone else.