tRode a 5400 mile road trip back in 2014 single speed, chain tensioner on a regular road bike. Crossed the Appalachians going both directions with no problems. If I remember I was riding a 52x19 for the whole trip with 40 pounds of gear in a backpack.
After having the chain tensioner break on me in late February 2015 I came up with a slick way convert the road bike/vertical dropout over to a fixie and have been riding that bike fixie ever since, way north of 10,000 miles since the conversion.
I was going to do the bike trip in 2015 fixie but I ended up getting a heck of deal on a brand new 2010, never sold, Specialized Secteur that had the rackmounting options on it and I knew since I live by bike, not car for almost 7 years now, I needed a back up bike and only pay for $525 for a brand new bike with warranty, I couldn't be stupid and pass up the offer.
Yeah, I would do a fixed gear trip anywhere in the country. It just takes being in shape and learning how to route a trip so you avoid the worst of the climbing, even when you are routing from one day to the next and changing your trip agenda daily.