Changing your MAC will make older messages undeliverable, but that just means the connection will be momentarily interrupted until you establish new connections after re-connecting to the WiFi.

Why not just assign yourself a different internal IP? Because a. the router probably wants to assign you one itself via DHCP; and b. the router isn't looking at your IP address to lock you out; it's looking at your MAC address.

If your IP address is where in cyberspace you are, a MAC address is who you are. If you want to fool the bouncer, change your name, not your address.