Here's a timeline of Dr. Atkins' view on caffeine over the years ..
1972 Diet Revolution: Caffeinated beverages limited to 6 servings per day from all sources (coffee, tea, diet colas etc) UNLESS you suffer blood sugar swings and hypoglycemia. In that case limit was 3 servings. Note, a serving is one 8 oz cup, not a super-size 20 oz bucket
1992 New Diet Revolution: No caffeine at all during the 14-day Induction period, then may slowly and cautiously add it back if tolerated. On p 309 he wrote, "... caffeine stimulates the insulin mechanism, and that's your vulnerable spot. It raises blood sugar at first and then allows it to crash. ..."
2002 New Diet Revolution, revised edition: The "no caffeine at all during Induction" rule was softened to simply "avoid excess caffeine". Excess caffeine was considered anything over 400 mg per day from all sources. (note, this is the current advice still given by Atkins Nutritionals).
For what it's worth, caffeine has never interfered with my weight loss efforts, including back in the low-fat dark ages
One significant issue with caffeinated coffee has to do with blood PRESSURE. Caffeine can trigger a spike in BP that lasts for several hours. This has been my personal experience, although the spike is less now since I've removed 60+ lbs. If you have a home BP monitor, it would be worth checking to see if this is an issue for you. Check your BP before caffeine, then 1, 2 and 3 hours after. I now limit caffeinated coffee to two 10 oz mugs in the morning only.