If you issue an ALTER SERVER command and there are active connections with that server in use or new ones are coming in, what happens? Docs on this command say nothing regarding active processing using the server context and changes to it. So I assume it's just handled.
Not sure if there are exceptions but assume that nothing external will change your current active session’s settings out from underneath you.
For example if you alter user/password, I assume that as long as prior user password is still good that actively running processes will keep going.
If you alter a password the old one is by definition no longer good...but it doesn’t matter because authentication only happens once - during login.
David J.