Looks like it will function OK to me. I would use a audio taper pot on the input signal to give one a volume control. Keep in mind that there will be some 'cross-over' distortion in your output when the signal passes through 0vdc and neither transistors are conducting. 'Hi-Fi' class A/B amps usually apply a little dc bias such the both transistors are conducting a few milliamps with zero signal so that there is a smooth transistion between positive and negative cross-over. However as you are feeding this amp stage square waves anyway it's not like you won't have terrible odd order harmonic distortion anyway. Now if you did some low-pass filtering before the input stage and fixed the cross-over bias you might get musical quality tones through the thing.
Lefty