One to two hour rides are definitely do-able on the Atkins diet, especially with a sports drink and some figs. I don't think a long ride (3 to 5 hours) would be however unless you were basically eating carbs the entire ride. Which probably is not a bad think since you are hopefully burning them off immediately during the ride. I've know a couple of people that have tried a modified Atkins Diet and kept up their cycling (120 - 200 mi/week). They basically did the diet except they ate a healthy dose of carbs about 3 hours before their long rides, and supplemented their rides with some type of carb sports drink during the ride, plus some fast acting carbs while riding.

I think the main concern regarding Atkins and cycling, especially long distance or endurance cycling, is that you can actually get to the point where you body starts breaking down muscle for energy during your rides instead of fat. And that is very unhealthy. The main way to avoid this is to keep your riding at low intensity so your body has the time to use the available carbs or fat, instead of trying to cannibalize muscle.

High intensity workouts with low carbs is actually a bad thing. It might feel good, but in the end you are really burning muscle, not fat.

Good luck with the diet.