Yes, that's correct. Once you submit your BOWP application, and as long as your PGWP is still valid at the date they receive your application at Vegreville, you are under implied status.
You won't be able to renew your SIN until you get the BOWP, but you can continue to work until a final decision is made on your BOWP application.
Your company might be asking you regarding your SIN. In my case, I gave HR a copy of my BOWP application along with a copy of the receipt and showed them the CIC processing time website with the 110 days processing time for paper BOWP; they were OK with that and just asked me to provide the renewed SIN as soon as I received my new permit, and so I did.
I strong believe that, if you submitted all required documents and meet all your immigration class requirements, you will receive a confirmation on your PR by October.
But if not, send your BOWP right away on the first week of October and you will be fine for another 3 to 4 months :