The alarm is likely to be running at 868 MHz which sounds totally different to the 2.4 and 5 MHz bands used by WiFi. However, when transmitting the output power could be enough to saturate or swamp the front end of your WiFi receiver on the router - so yes it could be a potential problem.
At least if you cable to a WAP you should remove that possibility.
M H C
taurus excreta cerebrum vincit