Unless someone who has actual experience provides an answer, the best the rest of can do is guess.
When my wife and I were putting together her outland application, we were faced with the same issue. She needed a pcc from her home country, Philippines. We had that to hand. She also required one from Hong Kong. The IRCC instructions and guide advised that for a Hong Kong pcc, we would have to file her PR application and await instructions from the IRCC, then send those instructions to Hong Kong, along with Hong Kong pcc application form. So, it was not a problem not having it when filing. Next, she required a pcc from the United Arab Emirates, issued by Dubai police. It was clear from the checklist that the IRCC expected it would be sent with her PR application. We had been working on getting it, but the process was time-consuming and difficult.
Our document checklist advised that, if any required documents were not submitted with the application, we should provide an explanation. We debated sending the PR application without the Dubai pcc, explaining the difficulty and saying we would send it when received, just as you are proposing. We wanted to get her application in as soon as possible, to get into the queue, so to speak. In the end, we chickened out and decided to wait. We had heard horror stories about applications being returned as incomplete, for the slightest defect, and the time lost. We worried that, even if no one looked at her application for 3 months and we sent the pcc in after 2 months, we would still be told the application was not complete when received and we would have to start again, meaning maybe a time loss of 3 months or more. I posed the question here on the forum, as you have, and got no answer.
Maybe someone here has done exactly as you propose and it worked out. Maybe someone tried that and had their application returned. Maybe someone with either experience will respond. For us, we just found it too risky. So, we lost quite a bit of time, including the time eventually taken for us to travel from the Philippines to Dubai to get the damn thing in person. We then sent it with her PR application.