No, the icecream has high fructose corn syrup which is sugar.

On induction you can only have the things on the induciton allowed list. Icecream dieffinetly isn't there.

Acceptable foods
http://atkins.com/Archive/2001/12/15-464579.html

Rules of Induciton
http://atkins.com/Archive/2001/12/15-325810.html