NAFTA TN to family sponsorship

[B and T]

Hi everyone,

I am wondering about whether the following scenario is permitted and doable (with respect to dual intent):

Is it possible for a US citizen to enter Canada on a TN visa, live with his girlfriend there, and while on the TN, apply for permanent residency via a spousal or common law sponsorship (assuming they are eligible)?  I have read that the TN does not allow dual intent, whereas a work permit does.  Does this mean that using the TN to work in Canada and then possibly eventually applying for PR is not allowed?

I can't seem to find any definitive information on this.  Thanks for any input anyone has.

- B and T