Funnily enough this may actually have a positive impact
People used to create tinfoil, tin can or wok based reflectors for WiFi to guide the omnidirectional signal into becoming a directional one.
I think the reflective part of some mirrors is essentially tin foil, so it probably would have a mild boosting effect in the direction of the mirror
Edit: in fact if OP’s fan has a rounded metal cage on it, you could take the front half off and you’ve basically got a WokFi setup there, with added danger