Whole question in the title, don't know what more information is possible:
Is an AB amplifier feedback like this possible?
Yes, it's possible. However, without doing a detailed simulation (or building the circuit), it's hard to say whether or not the resulting amplifier will be stable. My guess is, it probably will be.
Although, I have to ask, why would you want to? The TDA2030 will already put out about as much power as the power supplies allow. Your output stage won't do a whole lot better, and maybe even worse.
ETA: Oops! It probably will not be stable. Even without the added delay of your new output stage, your closed-loop gain (21 dB) is too small. Data sheet says minimum of 24 dB.
Any amplifier feedback is possible; whether it does what you intended it to do is pure speculation. It looks like it should work as a linear amp but, if you expected positive feedback and some kind of oscillation then you may be disappointed.
Having said all that, why aren't you using the recommended power-booster circuit in the datasheet: -