The short answer is no.
Push-pull means the output stage is has complementary devices that alternately control about half the signal by sourcing and sinking current -- not voltage -- between the positive and negative voltage rails. How much of the signal each control depends on the biasing so both Class A and Class A/B amps are push pull.
The term differential is usually applied to the input stage, where two transistors share a common emitter load or current. Each transistor is fed a signal (source and feedback, e.g.) and the difference is amplified and then converted to current and sent to the voltage amplification stage. The VA stage then sends the voltage gain to the output stage where the push pull takes place (the OS is a low impedance load that has unity voltage gain and current amplification). The current is then sent from the positive (red) terminal to the speaker with the voltage referenced to ground. The current is in phase with the voltage.
When the two channels of the output stages are bridged, one channel receives the input signal in the normal fashion and the other channel receives the signal inverted. Both channels still operate in their differential input and push-pull output stages as they would, however the output voltage is mirrored (i.e., fully balanced). But the difference is that the inverted channel's red positive output is connected to the negative terminal of the speaker.
The speaker is no longer referenced to ground. It is referenced to the negative voltage of the inverted signal channel. Since each channel is out of phase, the peak to peak voltage is doubled. Therefore the power is quadrupled (power supply willing and able, of course).
The reason it is not push pull is because the current is not sourced between the two channels through the speaker load. The current is simply doubled through the speaker and in phase with the positive (non-inverted) channel.