Any manager which cares about their employees would say that, "you should have come to me sooner." Only issue is how many managers are actually empathetic?
At the line manager level, probably many, even most. Empathy is selected against for promotion at most corporations, so if the OP is reporting to someone who is already a senior manager or aspiring to become one, it's unlikely.
That said, even the most cold-blooded bastard is going to make an effort to keep any middling-or-better employee right now. It's too hard to find competent replacements.
IMO it depends on the employee. I have some where I'd for sure go to bat to keep them around. I have some who slack off, put in minimal hours, and do a terrible job checking their work. They're a net positive, but barely, and if they were to throw a fit like that I'd tell them to take a hike.
That said, even the most cold-blooded bastard is going to make an effort to keep any middling-or-better employee right now. It's too hard to find competent replacements.