Yes, it is a push pull design. 4.5 watts sounds about right. I was guessing comparing it to a 4 output tube amp that uses 6V6 tubes which are the same as the 12V6 except they use 6.3 volts for the filaments instead of 12v. The amp I'm comparing it to has two 6V6's parallel, 2 for push and 2 for pull (and a lot more). It's about 12 watt.Tony, you are correct. I recall hearing these referred to as a push-pull amplifier, where one tube amplifies the positive portion of the output wave and the other the negative portion.
The tri-five Wonderbars and pushbutton radios used this same circuit. (The main difference between them is the signal seeking portion of the Wonderbar.) The manual tune radios used but one tube to drive the speaker.
Some '57 pushbuttons (like the one in my '57) used a single transistor to drive the speaker. They also use an unusual group of tubes in the remainder of the circuit that use a plate voltage of 12 volts instead of roughly 100 volts. These radios are a single piece unit (instead of 2 piece) and do not require the mechanical vibrator tube and transformer. FWIW, I also have a '57 pushbutton radio that is all tubes in my stash of goodies.
As far as output power - 4.5 watts sticks in my mind, but I can't remember where I saw it. I might have that in a paper copy book on these radios.
Problem with those early transistors is that they were made with germanium not silicon and they sometimes start to crackle and you hear a little static from it. The even degrade just sitting on a shelf, so a new one may be better or worse, If it's available.