Probably easier to just observe that, if GPT-3 isn't reliably correct, then it's not consistent enough to simulate a Turing-machine and therefore isn't Turing-complete.
As for loops: a Turing-machine could do infinitely many loops, so Turing-completeness implies that a system can do the same. If GPT-3 can't do infinitely many loops, it's not strictly Turing-complete; and if it can't do many loops, then it wouldn't seem like a meaningful approximation of a Turing-complete system.
As for loops: a Turing-machine could do infinitely many loops, so Turing-completeness implies that a system can do the same. If GPT-3 can't do infinitely many loops, it's not strictly Turing-complete; and if it can't do many loops, then it wouldn't seem like a meaningful approximation of a Turing-complete system.