Is an AB amplifier feedback like this (image inside) 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.