I don't think photoshop knows what monitor I have plugged in, or it's current settings, so I'm not sure how that would be possible.
I'm thinking of the tool that converts an RGB image, open in the editor, to CMYK. If your on ABCwebsite.com, and everything looks fine, then open Photoshop, click on CMYK preview ..printjob image looks drab...tweak the image..close image..open web image..work on web image..isn't that one size fits all?
If: 1. CMYK plays no part in your print workflow; 2. There is no such functionality in Photoshop, (now or previously), then I have no idea what to suggest