Mac addresses never leave your house. It might be possible to change the mac address but it depends if the software allows it. Maybe if it was hooked to a pc you could do it.
There likely are tricky ways to use a wifi repeater/bridge to make it appear that all traffic is coming from that devices mac address rather than the stuff connected behind it. The only reason I have ever seen to do this is when someone was trying to use it in a hotel and you could not directly use the hotel wifi. Mostly because you needed to respond to a web page which pretty much only worked with a pc.