MOSFET switching Gate Drive Voltage less than Load Voltage

You betcha.

Very little. The low drain voltage during switching will result in reduced impact due to the miller capacitance. As a consequence the effective gate charge that must be supplied/sunk by the gate driver during switching transitions will be slightly less than if you were switching a higher voltage. This is normally considered benficial since it means you will need a slightly wimpier gate driver circuit for a given switching speed, but the impact is fairly minimal.

Just make sure your two supplies share a common ground at the source. If they are isolated, you could use a gate drive transformer.

Also it your 7.2 volt signal has a high source impedance, you might pickup swtching noise that jumps through the gate causing spikes in the switching edges of the drain signal.