to the best of my knowledge (from people I've seen around me) you can't renew your SIN till you get your PGWP. You will be on implied status once your study permit expires (along with your SIN) so you should be good to work till you get your PGWP and can renew your SIN. Hope this helps, like I said, this is what I know from the number of people that have gone through the same process in the past.
I confirm. Applied May 21st, got, Study Permit and SIN expired on July 30th, so technically I am "implied status" (waiting for review), once pgwp I can renew my SIN. Currently working, but afraid my kids will not be able to start school if the pgwp decision takes so long.