Sorry, no.
A CDL brings down my legal BAC whether i'm in a commercial vehicle or my private vehicle.
My license allows me to drive any "one" vehicle of any weight - a triaxle dump, say, for personal use or for hire.
And I cannot tow a trailer exceeding 9,990 - it's specifically stated as such on a CDL class B. Class A is tractor trailer, so trailer weight isn't limited by one's license.
My license isn't different depending if i'm working commercially or for myself in a personal vehicle.
Like a bus - the SAME vehicle, as a 'bus' you need a CDL. If it's registered as an RV, any old license works - even if it's well over 26k pounds or has air brakes.
CDL's are so specific I can't drive a manual transmission commercially unless i take the road test in a stick shift truck or bus.
If you go for your class b test in a tractor (as in semi) with a fifth wheel they won't let you use it. take off the plate, and you can use it for the test. Absolutely no difference in the vehicle's size, handling, rules of the road, etc - but the plate on the back makes it a Class A vehicle - even without a trailer!
Hey, license's are government things - they don't have to make sense.