Thanks everyone, but none of these actually answer my main question -- can the baby come with us back to Canada while we apply for its new status?
Hi On-Hold
As you and your wife are PR in Canada, if the baby is born in Thailand... you will have to apply to sponsor your child to Canada, and one of you would have to remain in Canada during the sponsorship process.
You can apply for a TRV for the child while you wait for the application to be processed... but it can be very difficult to obtain as the baby would have a strong reason not to leave when the TRV expires as both the parents would be in Canada.
If you intend to go this route you will have to ensure the visa office in Thailand is aware that you are applying with Dual Intent... and advise them in the application that the baby won't overstay the visa and jeopardize the PR application.
Personally I think you are better off to have the baby in Canada, get the baby's passport and then your wife and baby could go to Thailand and travel freely back and forth once the baby has Canadian Passport.
Totally a personal decision you and your wife have to make.