Probably the same thing that happens if they somehow find a way to block the chips on all the other flashcarts out there. Guessing "blocking a chip" is one of those borderline impossible things for them to do though, even if it IS an easy thing to say... since if they were able to do such a thing, they'd just dismantle an acekard, see the chip in it and block it and kill the entire ds rom scene.
If you meant blocking the processor... not possible. The processor doesn't do anything to the DS, it's like a small minicomputer built onto the flash cart... I imagine the anti-AP simply watches the ROM data being read, and if it ever reads an address expecting a certain result and tries to freeze for finding the wrong value, it alters the value to what's expected (if that makes any sense...?). Just an assumption though, I've the bare minimum of knowledge on how such things might work.