Atkins only limits the amount of salad, and other low-carb, low-glycemic veggies, for the first 2 weeks.
If you're going to follow Atkins, Induction (the first 2 week period) is important, as you're abruptly changing your diet, and your fuel source... Atkins describes it as you're going from a diet that tilts heavily to carbs and sugar, to a healthy diet... so you have to drastically tilt your diet the other way... almost no carbs... to rebalance yourself for your new lifestyle diet.
After that, as long as you're watching your carbs, you can certainly eat more salad, and more "allowed" veggies.