The ATmega328 chip is rated to 5.5 V, with an absolute maximum of 6.0 V. If you want to be safe, put a diode between the + terminal of the battery pack and everything else. The diode will drop around 0.6 - 0.7 V. In addition the transistor switching the pro mini will drop a few tenths of a volt, if properly saturated.
One drawback of your circuit is that "ground" is not well defined for the processor and anything attached to it, since there is a voltage drop across the grounded transistor. That can cause difficulties, especially for circuits that involve radio frequencies. For this reason people usually use PNP transistors to form a "high side switch".