Can you match background color/tone in camera raw for headshots?

Yikes. The solution is to fix your lighting and exposure. You need better fill (reflector or fill light), a preset color balance (buy a ColorChecker Passport and use it!) and manual exposure. There is no excuse for that kind of variation in a portait setup.

Go visit the Strobist strobist.blogspot.com

One question…are all yearbook shots made with the same camera exposure locked down in Manual mode, or is using any automatic exposure features (Auto, Program, Aperture Priority, Shutter Priority…).

I'm not a photographer, so my first question would be – can this be normalised in the original shoot, rather than post? I imagine you have much control over the conditions - tripod, subject positioning, consistent studio lighting, exposure, white balance etc.

The backdrops are different, I get it that you don't want exactly the same one for each shot... Perhaps you could take a controlled shot of the background before the subject is shot, then combine the two in post?

Fully or mostly desaturating the background will help to align the photos when placed on the page, but there is still a major difference in their luminosity levels, some darker or brighter than others (which is obviously more of an issue than the colour variation).