I think he stays.
Why?
He's too much like Vermeil. Vermeil SHOULD have stayed, but when they made Martz the heir, Vermeil left so as to avoid any friction and make the change go smoothly.
McVay is the same way. If he was truly going to go, he'd already be gone. It's one thing to say to guys "hey, if you wanna find a new gig, feel free" as that may also be a way to clear out the roster of coaches without causing issues for guys getting hired since they're not technically fired and most folks looking at our situation will see our injuries first and any positional issues a very distant second if not farther down.
Also, I can't see McVay dithering on this only to leave the Rams with few options to replace him. Does anyone think the Rams wouldn't be interested in Harbaugh and/or Asshole Face not to mention DeMeco Ryans and a few other coaches if McVay left? Those guys will likely be wrapped up within the week...
So yeah, I think he stays