Yes they do. I don't remember what season or episode# it was, but the three of them came over to the US and flew down to Florida.
In this episode, they were supposed to buy a car in South Florida (Miami?) for something like $1500 and drive them to New Orleans
The trip was a complete hoot with only Captain Slow having AC (until Jeremy broke it of course.) They stopped somewhere in Mississippi (?) and painted each others cars with different slogans.
Hammond's truck had "I'm Gay" written all over it, Clarkson was driving a mid-80's Camaro with "Nascar SUCKS" written all over it and May drove a late 70's early 80's Cadillac Fleetwood with "Hillary for President" written on it.
Best part of the episode was when they stopped for gas somewhere in Mississippi.
Southerners really don't like people with "Nascar Sucks" and "Hillary for President" painted on their vehicles (forget about the over the top "I'm Gay" on Hammond's old Dodge pickup.)
I had tears running from my eyes I was laughing so hard at the gas station scene.
Still my favorite episode of them all, and I give the BBC 30 days before they cave and announce Clarkson, Hammon and May are back next season.
Top Gear is seen in over 150 countries (read that somewhere...) and is Britain's #1 export around the world. The BBC has to wake up and realize where their revenue's coming from and the truth is, that show is NOTHING without Clarkson. May and Hammond know it too.
The BBC doesn't have to worry too much about funding... it's paid for by the govt. and a $215 yearly license fee (aka tax) on every TV...