Because of the huge wait times, a lot of US applicants have sent applications without police clearances, citing the 3-4 month wait.
My application went fine without it. I got my FBI clearance after SA, and sent it on to Ottawa. In my application I included a note that I had applied for a police clearance and when I estimated to get it, and that I would forward it on immediately.
When I ordered my notes last week, I saw that they had attached my FBI clearance to my application, even though they haven't gone through it.
I did this at the urge of other applicants, who had done this with either the police clearance or medical, and their PR was approved w/o incident - probably because they don't need those forms until the very end, anyway, when they process the sponsored's application and make a decision
Best of luck! I urge you to consider sending it on instead of setting yourself back months and months.