Can co-authors check the status of a submitted manuscript with various publishers?
(probably more suitable as a comment, but I lack the reputation for that)

"Are there exceptions to this rule of thumb?"

At least some publishers that use Manuscript Central allow this. I am a non-submitting, non-corresponding author on some RSC and ACS papers and can view the basic status of (and download copies of) these manuscripts. It uses email addresses/ORCIDs to link these to your account, and you may have to have created an account with the relevant publisher prior to submission for this to work.