So, you know the MS aspect of PBF won't be a problem. Walks in the park, walks through your neighborhood, etc. Be a primordial gatherer and walk to the store for dinner, if the store is in walking range. If all you've got is a treadmill, get on it and if you have a rambling hills setting, well, there you go.
I don't foresee a problem with any of the 5 Essential Movements. You may need to accommodate your growing tummy with the pushups, maybe do them inclined rather than flat, depending on the baby's size. With my first baby, that wouldn't have been an issue until the 8th month. (She's very slender and petite, calmly waiting to be born.) With her little sister, though, I would have got to inclined pushups starting about the 5th month! She was a couple inches and a pound heavier, and she was just all over the place in there. You'll be packing about 20 extra pounds for the pullups near the end, so you might need a little assistance with your feet on occasion. Or you might just grit your teeth and do it. I do my overhead presses with a barbell. Just couldn't do Mark's methods and finally just grabbed a barbell and did it. If you're doing it the way I do it, you may have to slightly adjust for balance, but I don't forsee a problem. Even the planks can be modified to suit your situation. I think squats are perfect to prepare you for labor. You need strong legs for all the pushing that's going to go on.
With my first child, I was Xenia warrior mommy before I know what was going to happen. I told the nurse I didn't need an epidural. It hurt, but I wanted to be all natural. Until the midwife announced the OB was coming in because my baby was breech. So, I ended up with that epidural anyway, but a quick c-section and I was holding my baby within 15 minutes of the OB's arrival.
I will say that it's very important that you care for both yourself and your little one while you're exercising. But, if you doctor approves and you go about it responsibly, I don't see this causing trouble. I think it might make the birthing experience easier for you to some degree.
Motherhood: When changing from pj pants to yoga pants qualifies as 'getting dressed'.