There is some previous talk about this.
Alarm I/O LED Floodlight
Probably easier to relocate the motion sensor, since you would need to have that that full current switch in your setup somewhere anyways.
You would also have to account for the trip times on the alarm not usually being configurable, and usually only last a second or two.
You could also get some other system in the mix like zwave and stuff, keeping in mind delays on those can be annoying sometimes, but not bad.