I read that in order to be a member of the common-law partner class in Canada, you need to cohabit with the sponsor, be the subject of a sponsorship application, and have temporary resident status in Canada. Since she overstayed her visa, wouldn't she automatically be denied?Yes. IRCC and CBSA will immediately know she's out of status once the PR app is submitted.
As mentioned, they may or may not act on it, every case seems to be different.