My assumption is that HR would be irritated to find out he was doing that. Legally, I assume 'at will' handily covers it as long as nobody being targeted is a member of a protect class.
Personally, I do sort of understand his view. He does not like to put anyone on a PIP, and by the time he gets there, he has already concluded that the relationship is not saveable. In his mind, everyone involved should know that the PIP is a formality, and ideally they'd use the time to find another job and have a smooth transition. HR probably would not agree to firing someone with a few months of severance.
Depending on the company, that could easily be appealed/disputed.