No. It was built by western states and diplomats. It did however let some Nazis in to the command structure primarily because they had experience fighting the soviets. Both sides of the cold war started recruiting nazis around the 1950s which is why you start seeing tons of books from famous nazi generals about how they absolutely could've beaten the soviets. It was more or less a grift to get paperclipped to America or given an advisor position in a NATO country. The soviets also did this a ton too, the nazis in the warsaw pact just didn't need to sell books to get recruited.

https://www.reddit.com/r/tankiejerk/comments/1closlc/was_nato_really_built_by_nazis/