Hello,
For an initial or a recurrent regardless you will need TSA application and approval. You can absolutely do an FAA ATPL check ride in Canada, however make sure to coordinate with the training center and again TSA authorization is not an option.
I am surprised your previous school didn't send your for prints as they are mandatory the first time. Did you get authorization in the past already? If yes, then I wouldn't worry about it. If your previous application was denied, I would worry about getting fingerprinted.
Like Rotorhead1026 said: no FAA training, no TSA. but since you mentioned you will do an FAA type rating, then yes you definitely need it.
FYI, I am doing an FAA recurrent training in CAE Toronto on CL65 next week and I had to get my TSA.
MYH