The serial number is not connected to the WiFi address. There is a possibility that Acer/Gateway could identiify the MAC address of the WiFi and LAN adapters in the machine, but that is not very probable.
Your only real resolution is going to be a) reporting the theft to the police and giving them the serial number b) hoping your credit card covers the stolen merchandise (will require a police report) and/or c) the theft is covered by your homeowners/renters insurance (which will also require a police report).