I dont think this issue is related to the radar at least it doesnt appear that way on my system. You can have the radar on constant and just pan away from your hud and the FPS jump up. I'm pretty sure it has to do with the HUD when using FSAA and not the radar. If it was the radar then you could shut radar off and you would also see the slowdown in A/G mode as well.
If you load up a flight with a clean loadout (no missles) and go to A/A mode the issue disappears. If you load up just a couple of Aim9s or a couple of AIM120s then as soon as you go into A/A mode the issue appears again.
I am confident it has to do with the hud symbology for your missles in the HUD itself and how that interacts with your FSAA.

Try this: load up just the standard runway takeoff training mission with 2 AIM9m missles and go to A/A mode. once airborne fire off both missles while never leaving A/A mode and I guarrentee that as soon as your missles are off the rails and you are now clean your FPS will jump up to normal. Radar on or off will not matter.