Would the automatics eventually recover from any condition resulting from a jet upset? Stall/Spin? Inverted?
Depends what you mean by "automatics"? FBW laws? Or Autopilot?
The FBW Laws will restrict, or return, the attitude to within the defined parameters. What the limits are (if any) depends on what Law is being used.
To have got into a Stall/Spin/Inverted either requires the laws to have degraded already, or a severe external event that overrode the controls. In extermis, it reverts to an "Abnormal Law" if it fins itself in a "UP", in effect acknowledging something has gone wrong and giving the best option for a (manual) recovery.
So if all hell is breaking loose, would re-engaging the A/P and A/T be a viable option?
The engagement conditions of the AP are quite strict, so unlikely.
Will the FBW allow the pilot to pull excessive G?
Normally no, but in some degraded modes yes.
Contrary to some others here, I would disagree there is a strong requirement for an Airbus pilot to always understand these laws, and know exactly what they are. 99.9% of the time, you fly it like a normal aircraft, and get nowhere near the protections. The only drill I can think of where you "use" a protection is GPWS "pull up"? As the laws degrade, there is a simple sequence (Normal - Alternate - Direct - Mech) but in fact there are multiple "sub-modes" - and sometimes you will not know the details. ECAM gives you some hints e.g. some Speed Protection might be lost, but who in their right mind is intentionally going to fly the aircraft is a manner requiring "speed protection"? Ditto Stall Protection - are you really going to fly differently if this is active or not?