I do not think you could do that.
If you enter as a tourist, you cannot overstay. Sometimes they have something called Dual Intent (when you enter to study with a bonafide intention and, decide to apply for a PR, if you qualify... knowing that if you do not you'll have to leave the country after expiring the study permit and, after that, the work permit following the studies, when it applies). But in this case if she enters to stay, it's not going to be her true intention to "just visit". There's not dual intent, there's only a misrepresentation.
So in this case, I think if you'd like to sponsor her, she would have to be outside Canada.
And, it seems the way to sponsor your parents is to apply, and they select randomly from a base of candidates. Next time they do so is 2018, because they already did so this year. At least that's what I understood from here:
http://www.cic.gc.ca/english/information/applications/sponsor-parents.asp
To know more precise information, you could always search their FAQ and call them if you don't seem to find the exact answer.
http://www.cic.gc.ca/english/contacts/call.asp
Good luck.