Servo power switch circuit
Yes, that will work, assuming that the magnitude of the threshold voltage VGS(th) of the P-MOSFET is low enough. The gate voltage will be around -5.8 V = -6 V + ~200mV: the (relative) supply voltage plus the collector-emitter saturation voltage VCE(sat) of the NPN BJT.  

If you have a 5 V microcontroller, you could probably get away with removing the BJT and connecting R2 straight to the R1 - gate node. As few P-MOSFETs conduct at -1 V, you could just connect the gate via a protection resistor to the (5 V capable) microcontroller pin.