I've done the LED conversion swap too. Pain in the ass, but do-able.
But yes, a MK2 to MK2a display board will swap successfully.
In fact, what I did was to swap the display board from a spare MK2a into my Mk2 and swap the lighting kit over from my old Mk2 display board into my MK2 with the MK2a display board in it. Annoying but successful. I did it because my rotary encoder was getting flaky on the Mk2 unit, and I didn't want to replace the encoder because that was actually harder to do than swap the lighting kit.
Normally that wouldn't have worked, since normally the translucent rotary encoder knob would have been the wrong type: It would normally have been the round-shaft type from the Mk2 lighting kit, while the new Mk2a display board would have had a keyed-shaft encoder. However, I had once in the past, already frankensteined a keyed-shaft encoder onto the Mk2 display board so my clear knob was already the right type for the Mk2a board. The frankenstein job was the reason I knew how hard it was and why I didn't want to do it again.