Will this inverted switching circuit to drive 4 Ohm heater work?
See the diode build in Q1. It is forward polarized, so max voltage on Q2 will be too low to switch on Q2, and doesn't matter what would you do on G of Q1.
EDIT:
User Andrew Morton pointed that BS270N is a N-ch FET, so it's just a matter of schematic symbol used by OP. If this is corrected, then yes, the circuit will do its work. (Sorry for nasty schematic edit...)