No, it is not wise to submit an incomplete application. Generally an incomplete application will be returned to the applicant.
There have been some anecdotal reports of applicants who failed to include a police certificate when they should have, and the applications were nonetheless put into process . . . and then later they received the request to submit a police certificate (for the one report I recall more clearly, as I recall the request followed the interview). This tips the application process off the routine processing track and probably results in a delay significantly longer than it will take to obtain a U.S. clearance. (For many, the U.S. tends to provide the clearance in way less time than their website says. I suppose this probably varies considerably.)
What I do not recall clearly, but vaguely recall, is that I think in these reports the applicant did not check "yes" to item 6.M. but their travel history revealed that they had been in another country more than 183 days in the relevant four years. Thus the completeness check would not have caught the failure to include the police certificate. This is, of course, a significant discrepancy and could even be construed to be misrepresentation.
In any event, as usual, as almost always: When in doubt, follow the instructions; otherwise, yep, follow the instructions.
In other words, get and submit the clearance with the application.
(Side note: for the U.S. this is indeed a bit frustrating since we know that as part of the RCMP and GCMS background checks, the applicant is screened against U.S. criminal records databases -- virtually on a par with the background screening for any Canadian criminal history.)
By the way: Waiting and thereby having a bigger margin is almost always a wise thing to do. Three more months should be a decent buffer.