Did Canada have a real choice about whether
to enter NATO and NORAD?

Politically speaking, Canada did have a very real choice and could have rejected the offer to join them.

Explanation:

Realistically though, Canada became one of the founding members of NATO because of it's contribution and losses in World War II and how it believed that NATO could ensure lasting peace in the western world.

Similarly, NORAD was a join proposal from both the governments in order to provide better airspace defense. Canada did give more power to the US, e.g. the headquarters is based in Colorado and the Commander of the organisation will always be an American.

the answer is false.