When you are saying Atkins? I hope you are refering to something like BodyOpus or Anabolic Diet. This is a sure way to gain some quality muscle while burning up a good amount of fat. (CKD)
You basically eat no carbs, only FAT/Protein (70%/30%), for 5 days, then you carb-up for 2 days.
Here is a sample way of getting into ketosis and staying in it:
Sample for a 100lb person:
A) CALCULATION A (getting into ketosis 2-3days)
1)muliply >bodyweight x 12 = (X1)
EX: 100lb x 12 = 1200 cal
2) Multiply> bodyweight x .4 g/protein=(X2)
-> multipy (X2) by 4, which equals amount of cal from protein...ex: 100lb x .4 = 40g (protein a day) x 4=160cal from protein
3)Subtract > X1 - X2 = (X3) Cal in fat needed
ex: 1200 - 160=1040cal
4) Divide> X3 divided by 9 = grams of fat a day needed
ex: 1040 divided 9=115 g fat
->you see, here the ratio is about 3:1 fat/protein
B) CALCULATION B(staying in ketosis after 2-3d)
1)muliply >bodyweight x 12 = (X1)
EX: 100lb x 12 = 1200 cal
2) Multiply> bodyweight x .9 g/protein=(X2)
-> multipy (X2) by 4, which equals amount of cal from protein...
ex: 100lb x .9 = 90g (protein a day) x 4=360cal from protein
3)Subtract > X1 - X2 = (X3) Cal in fat needed
ex: 1200 - 360=840cal
4) Divide> X3 divided by 9 = grams of fat a day needed
ex: 840 divided 9=93 g fat
Yes, you can gain quality muscle while on "gear" and using CKD, as long as you have the carb-up's then it's a very good diet. But, otherwise, without insulin it's hard to say that muscle gain is a possibility.
Mr.X