ride4fun, I don't see any reason you couldn't do a "backroads" tour like this on mountain bikes. In fact, that is probably what I'd do a ride like this on. I know it would be faster on a roadie or cross bike with wider tires, but I prefer the comfort of a MTB on anything unpaved. You could always change out the knobby tires for something with a bit less tread (not slicks but something in between) to gain a bit more speed.
Emily
2011 Jamis Dakar XC "Toto" - Selle Italia Ldy Gel Flow
2007 Trek Pilot 5.0 WSD "Gloria" - Selle Italia Diva Gel Flow
2004 Bike Friday Petite Pocket Crusoe - Selle Italia Diva Gel Flow