If you are needing the 2n2222's because you need to drive more than 30mA with each, then that suggests possibly no.
However we need to know:
What current the 2n2222's will be supplying to their loads?
Is the Pro Mini powered via Vcc or Vin? In either case what voltage is Vcc and in the latter case what voltage are you supplying to Vin?
What else will the Pro Mini be interfacing to?
Given that can work out how much current is being drawn and what the voltage (if any) across the Pro Mini's regulator is.