Charging a 12.6V 3SLiPo from 5V USB (Or similar) voltage?
No that doesn't work. If you want to charge the top cell switching Q1 on (without current limit!), your Q2 (also no current limit) will pull Q1's base below the cell's negative voltage.  



This is your circuit for one cell. The signal coming from the microcontroller switches on Q2, but also is pulled down to 0.7 V. So the base of Q1 is also at 0.7 V, while it needs at least 5.1 V (0.2 V saturation voltage of Q2 + 4.2 V battery + 0.7 V base-emitter junction).

A solution could be to have a current output boost converter. This can generate a higher voltage from a lower input voltage. Constant current boost converters are often used as LED drivers.



Replace the LEDs with your battery, and set the charge current by choosing R1 = 95 mV/I.