Does the AOA and G-Force increase if a fighter uses the afterburner during a max G level turn?
TL;DR: Maybe.  Maybe not.  It depends on the particular fighter jet, and how it's loaded, and the effect will, in any case, be very small.

An increase in thrust causes an airplane to pitch up via two mechanisms (more details in this PDF):1


An increase in thrust causes an increase in speed; for airplanes with positive speed stability (which is true for all civil aircraft, but is often not true for newer fighter jets), this causes the airplane to pitch up and slow down.2  This changes the slope of the airplane's flightpath (making it point more up), but (at least at first approximation3) does not change its angle of attack.
If the thrust from the airplane's engines is not exactly aligned vertically with the airplane's center of mass, an increase in thrust will create a change in the airplane's pitching moment, which does change the airplane's attack angle; if the engines apply their thrust below the airplane's CoM (examples: 737, B-58), increasing thrust will pitch the airplane up to a higher AoA, whereas, if the engine thrust is applied above the CoM (examples: DC-9, Learjet 23) increasing thrust will pitch the airplane down, decreasing the AoA.  Most fighter jets have engines that are very close to the vertical location of the CoM, so the change in pitching moment from a thrust increase is very small, and its exact direction and magnitude will depend strongly on the specific aircraft and loading used (for instance, burning off fuel could change the vertical location of the airplane's center of mass - and, thus, the magnitude, and, possibly, even the direction, of the change in pitching moment caused by a thrust increase).


Thus, going from maximum dry thrust (no afterburners) to maximum thrust (with afterburners) could, depending on the aircraft, produce a slight increase in angle of attack and vertical4 load factor, but:


the effect would, at best, be quite small, and would depend strongly on the specifics of the aircraft and its loading;
with certain aircraft and/or under certain loading conditions, this effect could well be negative (in which case engaging afterburner would decrease the maximum achievable AoA and vertical load factor); and
the main effect would be (as you, in the latter part of your question, surmised could possibly be the case) to allow a high-G manoeuvre to be sustained for longer (due to the increased thrust helping to counter the high drag of a high-attack-angle manoeuvre).




1: For the purposes of this discussion, I am ignoring aircraft with thrust-vectoring capability.

2: Most airplanes will initially enter cyclic phugoid oscillations with anything other than a very slow, gradual thrust change, but the phugoid eventually damps out, and, even during the phugoid cycles, the "constant-attack-angle" part of the situation remains approximately true.

3: In practice, an airplane undergoing phugoid oscillations with a non-infinite period will undergo continual small changes in its attack angle, due to various damping effects, but the AoA does remain approximately constant.

4: Vertical from the aircraft's perspective, that is.