Contrary to what some seem to think, yes. It will still be a class-AB stage. Note that it is class-AB, as the diodes ensure some bias current without an input.
Q2 is backwards biased, which means that its collector and emitter are reversed and it will conduct in the reverse direction.
In practice what this means is that instead of a beta of, let’s say 300, it will have a beta of 30 or so. Which in turn means that base current will be much higher than if it was connected properly.
The base-collector junction has a different doping profile than the base-emitter junction. This also means that its forward drop will be lower which, in this configuration, further increases the quiescent bias current.
The large imbalance between base currents of Q1 and Q2 will guarantee that the quiescent bias voltage of the output will be considerably closer to the supply voltage than it would otherwise be.