Bottom line, it is highly UNLIKELY IRCC will provide expedited processing so an individual will qualify for a particular visa to some other country. That really is how it is. Really.
And, after all, you probably do not really need Canadian citizenship for the job. American citizenship probably qualifies as well.
That said, there is (usually) no harm in asking.
In the not so distant past, however, an urgent processing request based on employment advantages abroad tended to signal applying-on-the-way-to-the-airport or seeking-a-passport-of-convenience (as in a passport that would, for example, expand career opportunities in countries other than Canada), which in turn tended to trigger elevated scrutiny and the opposite of expedited processing, resulting in non-routine processing significantly increasing the time line. Indeed, for a couple years this could be a factual basis for denying the application based on lack of intent to CONTINUE living in Canada, until the current Liberal government repealed that provision. But make no mistake, even before the Harper government adopted the intent-to-continue-residing requirement, applicants perceived to be applying-on-the-way-to-the-airport or seeking-a-passport-of-convenience tended to encounter higher hurdles taking much longer. And that was first formalized under a Liberal government when it adopted an Operational Bulletin which prescribed related factors to be reasons-to-question-residency (in other words, criteria triggering the issuance of RQ, or as many think of it, the dreaded RQ).
There appear to be more recent reports indicating that factors which might give the impression the applicant is applying-on-the-way-to-the-airport or seeking-a-passport-of-convenience might not automatically trigger such severe non-routine processing these days. My sense is that is very much a IT-DEPENDS matter, depending on additional facts and circumstances, with strength of the case looming center stage.
But the odds are so low that IRCC will expedite processing in this scenario, asking for it is probably a rather foolish gamble.
FWIW.
