Does the White Tanooki Suit work the same in the Special worlds

I finished the main story of Super Mario 3D Land, and am working on the Special world levels now.

I die a lot (the levels are harder!), but I never seem to die enough in a level to have the White Tanooki Leaf appear so I can use the White Tanooki Suit.

Do I need to die more times in the Special Levels? Or does it not appear there? Or am I just not counting how many times I die properly?