Yes, the registered GVW in many states IS a legal, never exceed, limit.
It certainly is here in Montana, for CARGO CARRYING vehicles like my Dodge 1500.
The GCW is not, however, listed on the registration. Nor is the GVWR. In fact, you can have just about any GVW you want to pay for, REGARDLESS of the GVWR!
It has been over 40 years since I had a pickup registered in Washington, so I don't remember what was on the registration, but I'm sure the rules have changed anyway.
I would have to go out to the motorhome to check for sure (and I don't want to do that, it is COLD out there!), but I don't recall any GVW shown on the registration. It is not designed for carrying cargo like a truck is. IIRC, RVs are exempt from GVW fees.