AlexGurvic said:
O, good joke... I think it's untrue, because I personally know people from Ukraine who have moved under FSWP much more faster.
By the way, I applied online for visitor visa on 2 January this year and I've got it on 6th January... Thus, all may happen
Visitor visas are a much simpler matter, therefore they are expected to be way faster. I still think the best course of action is to warn the VO of the pregnancy as soon as they contact you (via an AOR, if I'm not mistaken), and in case you receive a request for medical before birth, you should hold out on taking the medical until you add the baby to your application. This means a birth certificate (and certified translation), passport, photos and an additional CAD$ 150 fee, together with updated forms.
If the deadline for the medicals is getting close and you are still not able to include your newborn in the application, contact the VO and ask for a deadline extension, I'm sure they can accomodate that.
The alternative you proposed, getting your newborn a visitor visa and proceed with sponsorship, is messy and prone to complications. I would consider this a last resort if all else fails. If for some reason you get your CoPR during the pregnancy, I think you should rush to perform your landing and deliver the baby in Canada, and then you can go back to Ukraine and plan your actual move.