Depends on a few things. First, which players we manage to bring in, and second, what you mean by "turning this around". Because this is a multi-season project with or without Amorim, in my view. The squad is in such a bad state that even with a really good transfer window, I would not be expecting top four next season (again, from Amorim or any other manager).
But let's say we bring in Cunha + a quality striker and a good central midfielder, I would expect that we can see significant improvements to the performances and that we are well on the way to finish with around 65 points or more. If we start the season similar to this one, I'd expect his job would be in serious jeopardy around the same time of year we got rid of ETH (Mid/End October)
I think it's perfectly reasonable to question Amorim and in particular his system, but I think's it's bordering on delusion to think that another manager would have us anywhere close to the fun positions this year. I'll make this point again and again: The squad is really poor. No quality up front, not physically fit for the PL, full of youngsters, old men, sicknotes and frauds. No manager or system gets around that fundamental fact.