CLR is good stuff but pretty strong to leave on overnight.
It is probably fine, but I have had a few problems with it when left on too long, sometimes it can slightly damage the finish.
Maybe start with just bathroom cleaner to get the soap film off, then paper towels soaked with straight vinegar.
Put plastic wrap or some grocery bags over it to keep from drying out.
Or just use CLR and a gentle Scotchbrite pad.