Lots and lots of theorizing about how things should work and why.
To be clear, however, NONE of that is at all responsive to the OP's question or those posed by others making inquiry about the potential impact of leaving Canada for extended periods of time AFTER applying but before taking the oath.
REMINDERS responsive to the subject of this topic:
Traveling abroad, with a lot of emphasis on TRAVELING rather than moving or living or staying abroad for extended periods of time, is not at all prohibited or restricted. There are logistical RISKS however. These are real and should not be underestimated. Time to respond or appear can often be rather short for IRCC requests and notices, including scheduling for tests and interviews, but especially scheduling for the oath.
There are currently NO prohibitions or restrictions precluding PRs from living abroad (or staying abroad for an extended period of time), except the very liberal PR Residency Obligation. This is true for PRs with grant citizenship applications pending as well as PRs generally. For the PR with a citizenship application pending, there are again the logistical risks. Which, again, are real and should not be underestimated. There are additional procedural RISKS related to concerns about verifying the citizenship applicant's actual physical presence. The latter tends to be way underestimated by many of the observations posted in this and other topics about this subject.
And it is in this regard the discussions tend to wander astray of how things work, what is the better way to navigate the process, or what to anticipate from IRCC. There is more than a bit of
how-it-should-be underlying many of the observations as if
how-it-should-be determines
how-it-will-go.
And frankly, sure, more than a little
how-it-should-be probably does influence some of the decision-making. EXCEPT how that influences the decision-making does not depend on who has the better view about
how-it-should-be. How this influences the decision-making is not about which point of view is more right. It is about the point of view of those making the decisions.
While the point of view of those making the decisions is NOT all that easy to discern, since the decision-making is always framed in terms of eligibility requirements and determinations of fact directly relevant to the requirements, no great psychic powers necessary to recognize some of the more influential, albeit typically unspoken elements in bureaucratic decision-making.
The biggest influence of this sort is general credibility. So long as the decision-maker has no reason to doubt, question, or challenge the applicant's credibility, there is a very good likelihood of a decision based on the facts provided by the applicant in the application and calculation of actual physical presence. As soon as there is a crack in the extent to which the applicant can be relied upon to be a reliable reporter of fact, there is a growing RISK the process will go off on a non-routine processing track which, depending on the particular case, may result in lengthy delays or even a skeptical assessment of the applicant's case potentially resulting in a Citizenship Judge hearing, in which event it can come down to whether the CJ believes the applicant's accounting of facts related to presence or not.
There are many, many tangents in the factors which can affect a decision-maker's impressions about the applicant's credibility.
This leads to some of those which may affect how it actually goes for an applicant who has moved abroad while the application is pending. Questions: what impression does the applicant's case make? Does this applicant appear to be an honest, sincere, credible individual?
Let's be frank: if the overall pattern of facts suggest the individual applying for citizenship is seeking a passport of convenience, that gives the impression there is a MOTIVE to exploit the Canadian immigration system, and where there is a motive to exploit the Canadian immigration system, that suggests a MOTIVE to manipulate if not outright deceive. If the decision-maker gets an impression the applicant is exploiting the Canadian immigration system, seeking a passport of convenience, there is an increased
RISK the decision-maker, AT THE LEAST, will approach assessment of the claimed facts with an elevated degree of skepticism. This is real.
How much so? That is very difficult to forecast. Historical reporting has shown cases going in very different directions. Many who move abroad while the application is pending run into ZERO problems. No delays. No RQ. But many others do run into problems, more than a few encountering RQ-related non-routine processing that causes lengthy delays, some ending up waiting for a CJ hearing, some denied citizenship based on failing to prove actual presence. REMEMBER: the requirement is MORE than just meeting the actual physical presence requirement; to be eligible for a grant of citizenship the applicant is required to PROVE meeting the actual physical presence requirement.
No matter how much some believe there should be no negative influence in the process resulting in living abroad after applying, and indeed no matter how much that belief is right, the REALITY is that of course there is a significant RISK that living abroad is going to have a negative influence in, again AT THE LEAST, how severely the decision-maker scrutinizes the case.
For anyone who has doubts about this, two reminders:
-- for DECADES the criteria for issuing RQ, that is what constituted a reason-to-question-residency, EXPLICITLY included indications the applicant was living abroad while the application was pending; make no mistake, this was true under previous Liberal governments and indeed was an explicit part of the appendix added to the then governing Operation Manual for assessing residence under a Liberal government.
-- under a Conservative government, the statutory requirements were modified to include a provision that would allow the denial of a citizenship application on the sole grounds the applicant was living abroad after applying; while Trudeau's government promptly repealed this provision . . . it warrants revisiting how that all went down, and the sense that was more extreme and harsh than necessary . . . it did NOT reject the general widespread sentiment in government, or among most Canadians, that underlies strong suspicions about those whose application for citizenship is about seeking a passport of convenience.
OVERALL: make no mistake, there is a rather high RISK the applicant who barely meets the minimum requirements for citizenship, and moves abroad soon after applying, could be suspected of seeking a passport of convenience. They can still make their case and eventually take the oath. The RISK is the path will be longer and the hurdles higher.
This is just about the way it is. Regardless what one believes about how it should be.
Some of the discussion above is about what naturalized citizens have done AFTER becoming a citizen. NOT at all relevant to what the prudent applicant will do before taking the oath.