Hello,
You can be sponsored even if you are out of status, But i will strongly advise to extend your visitor visa, if possible. You don't wanna go that road, if you still have slight possibility of extending your visa. When you have valid visa and you apply for sponsorship ,then you can get your work permit in about 3-4 months but if you are out of status and you apply for work permit, then you have to wait till AIP, which is nearly the end of process. Also, if you are applying for common law sponsorship, you need to provide lots of proof for cohabitation for period of at least one year. Just be prepared and save every little bill or anything which show you are living together at same address. I hope it helps.