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Whole question in the title, don't know what more information is possible:

Is an AB amplifier feedback like this possible?

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This looks like class B. You do not have a biasing network there to go into AB; just a pair of diodes. – Kaz Apr 18 '14 at 23:37
The extra output stage doesn't have any voltage gain, so you are safe there. The overall loop could have a degraded phase margin because of this; but on the other hand, the closed loop has plenty of gain: it is not being asked to be unity gain stable. – Kaz Apr 18 '14 at 23:45

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.

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It was just a fast drawn circuit, because I wanted to know if it is possible. I am currently designing a 50Hz inverter for a school project. – th3falc0n Apr 18 '14 at 23:24
That still doesn't answer the question. Why the output stage? If you're building an inverter, I assume you're intending to use this to drive a ~12v transformer, and getting 110 (or 220) out of the primary. This really won't do the job. First off, your output stage won't drive more than about +/- 12 volts, which means your transformer secondary has to be rated at no more than about 8 volts RMS. When driving 12 volts out, the base drive for the BD911 will only be about 15 mA, and the minimum hfe is about 20 for this current, so you only get 3 amps out. (You might get more, but no guarantees.) – WhatRoughBeast Apr 18 '14 at 23:56
As I said I don't intend to use the given Circuit, it was just a short draw to ask this question, in the real design I will have to drive 12V with about 25 amps, and I am not even sure if I won't change to a class D amplifier. – th3falc0n Apr 19 '14 at 0:11
Oh crap, another typo. You'll only get about 300 mA, not 3 A. And this means the hfe is acutally a good deal higher, so you might get .5 A. – WhatRoughBeast Apr 19 '14 at 0:12
@th3falc0n I don't think the bias network is really necessary. At 50Hz the op amp has so much open loop gain that negative feedback will eliminate any crossover distortion. 2 transistors, with maybe a bridging resistor will do fine. – Bitrex Apr 19 '14 at 0:15

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: -

enter image description here

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