Can GAN transistors be used for class A or AB or just call D

Yes they can but they only come in N channel, no P, so you can't do a usual complimentary push pull.
Same reason but more so the P channel in normal Mosfet amp  is not as good good as the N but with GaN it would be even more so.
From memory Solution make and class a/b amp using just n channel Mosfets top and bottom, but there are other disadvantages doing this.
Cheers George   

Mosfets used in class D amps are non-linear, and almost always N- channel configuration, either half-bridge (Hypex) or full bridge (Icepower).   I'm not sure why there is no complementary pair designs.  All N-channel require charge-pump to provide voltage for the upper transistor, since its gate voltage is referenced to source voltage (changing output voltage).  Advantage of GaN transistors, as far as I know, is in the switching speed and not in the linearity, required for class A or A/B.
In general Mosfet transistors are designed into two separate categories - linear Mosfets and switching Mosfets.  Mosfets used in class D amps are pretty bad for class A or A/B applications.