Normally, I would say no, since the frequencies of the garage door opener (315MHz) is quite different from your wireless network (2400MHz). However, I've seen all manner of innocuous devices produce harmonics and garbage that will interfere with 2.4GHz. My favorite is a cordless doorbell on 433.93MHz, that produced enough harmonic garbage to stop my BEFW11S4v4 in its tracks for a few seconds. Changing the channel on the BEFW11S4v4 solved that problem.
Incidentally, the interference would come from the hand held transitter unit (key fob), and not the receiver located in the garage. The power is so low, and the distance presumeably so far, that I really doubt you will have a problem.