Do they?
If you are going for very low carb, I wouldn't use carrots on your low days. I always recommend Veggies with a Glycemic Index of 20 or less (Such as Broccoli, etc).
Carrots vary too much in all of the published lists and i wouldn't trust them. For example,
Carrots, raw (Romania) = 16 GI
Carrots, boiled (Canada) = 92 GI
(Results from glycemicindex.com)
Excellent vegetable if you're not looking at GI numbers though.