"Would the automatics eventually recover from any condition resulting from a jet upset? Stall/Spin? Inverted?"
Unlikely, since there are an too many permutations of logical states. In other words - the system is too complex to cover for all possible outcomes.
The only definitive proof that it could would lie in math field - prove it in math - it is 100% guarantee,
One counterexample also - Bus stall warning shutting itself below 60kt threshold, since the AoA readings rendered invalid/inacc. I doubt designers predicted/ thought about that )