I am not really convinced having absolute pitch will make you a better improviser than someone who has good relative pitch.
In most jazz music you will have the lead sheet so you don't really need to know anyway. Besides that, you don't really need to calculate anything if you have relative pitch. If you practice enough it's instant. If I hear a note or chord followed by another note or chord I can tell you their relationship in real time. Anyone who has done enough ear training can. In fact, it's one of those things where you either know instantly or you haven't practiced enough. I was never really in an in between state.
In most jazz music you will have the lead sheet so you don't really need to know anyway. Besides that, you don't really need to calculate anything if you have relative pitch. If you practice enough it's instant. If I hear a note or chord followed by another note or chord I can tell you their relationship in real time. Anyone who has done enough ear training can. In fact, it's one of those things where you either know instantly or you haven't practiced enough. I was never really in an in between state.