You have to be sure about your state of residence having your medical card on file.
If they screw up your license is invalid.
I think some states suspend you while others simply de-certify your CDL until they get it.
There have been a lot of drivers get jammed up on an inspection because of this.
Az is the worst I've heard of but they've all had issues...
mostly in the past but better safe than sorry.
Here in Missouri you get a receipt with a copy of your CDL and the DMV's submission to the state which I carry in my permit book along with my long form physical but it's totally worthless to enforcement.
I also carry my medical card as I always have but I think it's worthless to enforcement as well.