I would assume that unless you are able to deliver enough power to damage the receiver (and remember it goes down fast, r^2, plus transmitter is on the side of the microwave, standing wave perpendicular to the door), it wouldn't really impact transmission. It's not AM radio and you are not even outputting noise with timing comparable to transmission, just adding constant (or maybe 50hz sine).

Plus there are multiple channels at 2.4Ghz, and you are probably outputting a narrow single freq.

But that's just me guessing, I'd love to know if it would actually work.