Unfortunately, I don't think extensions are granted for ITAs or for eAPR (electronic application for permanent residency)( submissions (the part after you get the ITA). If you get an ITA next week, you will only have 90 days to submit the paperwork and eAPR; if you can't meet this obligation, you'll have to decline the ITA and go back into the pool to wait (hopefully) for a new one.
However, if you get an ITA next week, that would give you until January 17, 2018 to submit your eAPR and supporting documents. If your application is processed and approved within the 6 month timeframe, assuming you do your medical exams the day after you get your ITA, you wouldn't be asked to 'land' (claim your PR) until October 17, 2018 (the date your medicals expire), and you can add a family member to your PR Application, even if it's already approved, right up until the point that you land. Since your baby's due date is April or May, he/she would definitely be born in time for you to add him/her to your application. You would just need to ensure you don't land before adding him/her.
On top of that, there is a chest X-Ray portion of the medical exam that doctor's usually don't advise pregnant women to do (i.e. they will defer this part of your wife's medical exam until after she gives birth). You will be able to submit your eAPR in the meantime, but IRCC won't complete processing of your application until they get the chest X-Ray portion of your wife's medical, which means your application won't be approved until after your child is born and your wife can complete the medical.
Bottom line, accept your ITA, and submit your eAPR as soon as you can instead of delaying - all the measures that are in place to address a situation like yours will ensure everything works out in the end if you end up getting PR Approval