Can a nonresident American citizen get a Canadian helicopter license?
In the US it is a license as well, that's why they abbreviate it PPL and CPL. 

Canada appears to have no restrictions on flight training of non-Canadians other than proving your own with something like a passport, because your citizenship is shown on your license. See this Transport Canada page as a starting point. 

If you need to reside in Canada during your training and you expect to take longer than 6 months, you will need to obtain a Student Visa to remain in the country legally.  You could also use a Tourist Visa, neither of which would all you to work. 

If you are planning on returning to the US when you are not training, then the Visa would not be required.

Converting a Canadian pilot license to a US pilot license is governed by AC 61.135a.. It doesn't look very complicated, but it will take time and you must take one or more knowledge tests as well as schedule an appointment at your local FSDO for the final approval.

Note also that while you don't have to surrender your Canadian license when you convert to a US license, if you do not that means that you must stay current based on both the US and Canadian rules.

I suggest you very carefully study the requirements and do the full math. Once you get started on one path it won't be easy to switch to the other if you then realize it was a mistake.

Interesting question, BTW. It was fun researching the answer. :)