There's a reason why they're lesbians.
The child would be put into CBSA custody and the provincial child welfare office would be notified. If you are not subject to First Safe Country and/or a convention refugee you are generally brought before an immigration tribunal within 72 hours. If you are not deemed summarily ineligible you will be released (if you have no criminal record) into the community for a tribunal hearing in 2-3 years.
You can collect welfare and other medical insurance benefits during this time. Bear in mind that Canada has 10% of the US's population.
t. immigration lawfag in a previous career
Oh, yeah, Roxham Road is a huge loophole in the First Safe Country treaty. It's not a port of entry. Admirality Law. Quebec has no Roosevelt Easement (although I think they are fixing that with layiciy, getting the Holy See out of the control of the province for good with reincorporation. Quebec did this in 1981 as well but they didn't do it properly.)