An incomplete PR application would not affect my OWP+TRV extension application. Your implied status begins from the time you submit your application to CIC. I am pretty confident that both of my applications are complete and especially my extension+OWP application. I also attached a letter from my sponsor (my husband) stating clearly that he will be responsible for my stay until a decision is made. They already have the PR application + sponsorship forms which has the undertaking statement.
Despite this forum being amazingly helpful, I did consult an immigration lawyer and asked him to go through my application before I submit it. Their standard procedure for the cases they prepare includes the OWP+extension application in order to keep the applicant in status while the PR is being processed. They CONFIRMED this information by calling CIC from their office as I was also concerned about this information. OWP+extension costs $155 on top of your regular PR+sponsorship fee ($1040 in my case) and needs to be paid separately.
In short, you will have implied status. As for incomplete OWP+TRV applications, they don't ask you to submit the missing/incomplete documents, instead, they go ahead and reject the applications altogether. Your implied status will stay as long as you are applying for PR+Extension before your current visa expires.