On
I drove over the Chesapeake Bay Bridge last year with my 5er ($17!!). They asked at the gate if the propane was off, but didn't forbid me from crossing just because I was carrying propane. This is a bridge/tunnel (two tunnels).
My fridge will get pretty cool, and if I get it cold before I leave, and turn the gas off before driving, it will keep things from going bad (milk, cheese etc). However, it take too dang long for it to get the beverages cold enough again. And it won't keep anything frozen if gas is off while driving. I am in the military, and shop at the commissary. I get meat cheep, and so I buy it all before I leave. It has to keep frozen.
SOLER