I would not mention that you are her fiance. To get a TRV, she has to prove she will leave Canada, so she needs proof of ties to her home country. Showing she has a fiance in Canada will make the visa officer think she will not leave Canada when her visa is up.
When applying for a PR visa, the applicant has to list all applications to come to Canada (and other countries). If she gets a TRV, visits Canada, and then returns home, this will be seen as a positive for the PR application. If she applies for a TRV, and is refused, this is seen as a negative. Only one application is probably OK, though, and she should be sure to state that she wanted a TRV to visit you.