app to sponsor....

Technically all required documents are, duh, required. That's the way requirements work. Really, that is how they work.

Thus, technically the application could be returned if one of the checklist items is not enclosed. I think there is at least a fair risk of this happening if no police certificate is enclosed.

If it is a matter of an applicant having to submit multiple certificates, as in from multiple jurisdictions, the enclosure of one should get past that stage.

It is possible, though, that enclosing none may also get past the checklist stage and the applicant will receive a request from the visa office asking for the police certificates. I am not sure.

But, that said, this does not seem like a good idea.

Foremost, the way bureaucracies work it is almost always best to take the path of least resistance, meaning the path involving the least number of task-steps, as possible. Any additional step in the process is one more step where things can go awry, slip off the tracks so to say, including, for example, parts of the application getting separated and even lost. Not including required police certificates means, at the very best, the application is taken out of the routine processing line and set aside for making the request, receiving the response to the request, and putting the application back in queue to be processed. Should go OK, with a significant delay writ into it, but again there is, in this, a greater risk that something goes wrong in those additional steps.

Secondly, the delay likely to result at that stage is probably longer than it would take to wait for the certificates up front. Not necessarily, but applications removed from the mainstream process tend to go into extra-slow-mode queues, at least so far as I can glean from reports in the past.

Thirdly, and this may be critical: I wonder to what extent not including them upfront could raise questions . . . resulting in more scrutiny, perhaps a more intensive background check. I do not know. Really do not know. But I do know that incongruities are often the cause of heightened scrutiny generally. An applicant from the U.S., for example, may be additionally asked to submit state police certificates in addition to the FBI one. Now, most applicants have nothing to fear from any such added scrutiny, except the added delay which something like this may entail.

By the way, generally it is a good idea to submit everything in one application package even if one is talking about discretionary items or documentation. The time it may take to gather, compile, and submit all relevant documentation and information tends to be less than the delay that results from sending stuff in piecemeal. You are dealing with a bureaucracy, not a commercial business. They have lines of business and things always go smoother, more quickly, if one's case stays within the primary lines of business. Sidetracks tend to sidetrack things in life generally (that's why they are called sidetracks), but in bureaucratic processes things getting sidetracked have a significantly greater risk of really going off the rails.

Best to stay focused, to do it right, to be patient and send it all in one complete, well-done, well-organized package. Again, that's true even for discretionary stuff one might just want to also include, let alone for the specifically enumerated required items.