If all the computers are in your local home network, it should work. It does not matter whether your computers use cable or radio connection, so yes, robocopy does fine with WiFi. It just needs to, as it does not know whether you're connected by wire or by radio. Just like your browser does not care if your computer uses WiFi or an ethernet cable plugged in to provide the network access.
There is a little catch though, your internet router (the little box you have put somewhere) might differentiate between devices connected by radio (WiFi) or cable and it might separate these from each other for security reasons. But if your SyncBack Touch thing worked (kind of), you seem to be good, your router is very probably not configured to separate radio and cable connected devices.