GV60 Valve System: Yes, the remote and wall switch can be used together to turn the fireplace on and off, regardless of which is used to turn the unit on.
SIT ProFlame II System: No, the included remote and wall switch function independently. If you turn on the fireplace with the remote, it must be turned off with the remote, and same with the wall switch.
Honeywell Valve System: This does not ship with a remote or wall switch, but with a power cable that can be hard wired to any outlet switch, or even 3rd party smart devices. 3rd Party Outlet/Remote Options