sure, you could pretty much do anything thing you want as long as its a 12v signal. Hell you could even buy a 12v battery, they have them in AA size and use that with a switch, kinda depends what you want to do, but in the end it has to get the 12v from somewhere and the easiest way is usually tapping into an already switched 12v signal in the vehicle.
the remote wire is simply controlled by a low current 12v signal. Easiest thing to do in your case is to splice in a switch into the HU's remote wire. This way you can turn the amp on or off when the HU is on.