It depends on the amp. For amps that have passive output ground, there is no problem sharing the ground. But active ground or bridged amps cannot be used in this manner. You could verify this with a DMM. With the amp powered off, measure the resistance between the left and right output ground terminals. If you read near 0 ohms, then it's ok to share.
The main problem with using a speaker amp to drive headphones is that it most likely have too much gain, and therefore will be noisy (typical headphones are much more efficient than speakers, what's inaudible through speakers would be unbearable through headphones). Also, the high output may fry your headphones. The usual solution is to insert series resistors to reduce the output (as well as the effective gain), but that is also
less than optimal.