Can I feed my panel Control terminal with one voltage (120 or 277 VAC) and then feed the Sense Input with a different voltage?
While electrically this will work, it is not a recommended practice and would be suspect to the approval of the local jurisdiction. The goal with a sense feed is for the sense to be tapped as close as possible to the circuit feeding the loads. If the sense feed is 277 VAC but the control feed is 120 VAC, there must be a transformer somewhere providing the 120 VAC. If that transformer failed, you would lose incoming voltage to the panel, but no emergency state would be triggered as the sense feed would still be present.