I started Atkins in September of 2003 and lost about 20 pounds in the first 5 months. Since then, I've lived pretty much true to a carb-restricted diet, holding steady at about 100-120 "good" carbs per day. The weight has stayed off (note: I went from 175 to 154.)
Since going to the diet plan, I increased my annual mileage from 6500 to 8000, rode my first sub-5 hour century and averaged over 150 miles a week for the last 18 months. So I think it's safe to say that one can use a carb-restricted diet with an active cycling plan.
Simply, I modified the diet to meet my exercise needs. I stay away from bad carbs during the week, I eat a regular low carb breakfast supplemented with a dose of carbs (Pop Tarts) before my weekend 3 hour rides and I eat PowerBars while I'm out on the road. I no longer eat potatoes, rice, pasta, cookies, bread and regular soda as part of my regular eating plan. If by chance they appear on my plate (eating at friend's for example) fine. But I limit them and I don't prepare them.
You can do it, you just have to be smart about it. In the early phases, I was buring so much fat and getting so much energy from it, that I didn't need to carb-up at all. That changed once I became leaner and I did start eating during the rides.