[Outback Jess]

If you mean starting at the 2nd Phase of Atkins, "OWL" Which is Ongoing Weight Loss, you will find in the book as you read that when you start there you add ONLY 5gr of carbs in the veggie catagory and only allowed veggies. I am sure you can start there, because the unique thing about Atkins is the flexibility for all with in the boundaries of the diet.
I would say, go for it and see if this is works better with the inflammation you are feeling.
One more point, the fatigue and detox effects that we all feel during induction eventually do pass and usually within 4 or 5 days. I have personally experienced alot of headaches and terrible fatigue til my body starts burning fat for fuel and then everything gets increasingly better, bright and happier for me.