I received more or less the same advice you provide above—that is to say, the agent actually said 'we won't know if you leave the country', but that 'you shouldn't leave for long because your application could be considered abandoned'.
I'm not sure what to do with such vague advice, and it leaves me wondering, still: how much do IRCC and CBSA really communicate?
Are applications really cancelled when people travel, or is it mostly hear-say that keeps folks from travelling?
As
@Underhill noted, Canada - at least CBSA - does have instantly available info, for some time now (post 9/11). More recently government has announced they do have a system in place to know about departures by air.
But you did hit on the question: how much IRCC and CBSA actually communicate. And the answer is we do not know. We know IRCC
can get the information, but not clear whether they do this constantly / all the time or just when IRCC wants/needs the info. This also applies to info IRCC gets / can get from other agencies like CRA. Or whether IRCC gets info indirectly when they ask for security clearances (RCMP/CSIS etc), and how directly, and how quickly, etc. We don't know.
Agencies
can share info but - if I understand the legislation - they have to either have a reason or an info-sharing agreement in place. Even if they have legal authority to get information, it makes a big difference whether (for example) they can look it up themselves with a few keystrokes or have to fill out a form or can only ask for precise information and not 'all info.' (Privacy restrictions are taken seriously). And what's true today may not be tomorrow - if there's a technological / data gap and they fix it somehow, the situation can change.
A lot of info here is somewhat anecdotal - IRCC does sometimes find out people are not in Canada when they're supposed to be, and that has negative consequences (apps are cancelled/deemed abandoned); a lot of people 'get away with it' (apps are not cancelled but we don't know the reasons why in one case and not another); and this is a social network, not a database of all cases and so no-one knows. The law in some cases (IRCC laws that is) leave a fair amount of discretion - i.e. an individual must be 'resident' in Canada but the precise meaning is not defined.
(Also gcms notes from any source may not tell the whole story - what's a "record" and does agency A have to tell you what agency B has on you is not clear; do they have to report on records they know exist or do they have to 'own' the record to disclose it?)
In practical terms: we don't know if IRCC habitually checks this info, or just sometimes; if they only do it at certain stages in the process ("is the applicant in Canada
today?"), nor if they usually spend a lot of time considering whether an applicant/sponsor "is
resident in Canada" (today? habitually? do they have a good reason?) to make a reasoned judgment; or if they only look for this info and decide if there are 'other problems/questions' (undefined) with the sponsor/applicant file overall.
And again in practical terms: they literally could turn a switch tomorrow and decide to be much more strict. (Either because it becomes less costly to look into the issue, i.e. a technical fix is found, or because the government decides "this is important and we've been too lax.") Or, to be fair, the government could decide "covid is a bloody mess and let's ignore this issue unless the applicant/sponsor is flagrantly breaking the rules.
And if they decide to be more strict or less strict, do they do so on some simple rule like "one month is fine, three months is a 'fail.'
So, you have to decide yourself. IRCC and CBSA can have different approaches (eg IRCC decides they don't care and won't check, but if CBSA doesn't let you back in the country, doesn't matter).
The 'rules of thumb' here could be wrong and no-one would ever notice or care; but if IRCC/CBSA 'catches you' (in any of the scenarios above), you may not have any real, practical recourse.
Meaning, sure, you could try to go to court, but it might cost tens of thousands of dollars and take years and still be uncertain and at that end, all you've won is the right to (effectively) re-start your application; or you could do what is often the only realistic option and just re-apply (and all you've lost is 6 to 18 months).
(Just my opinion and I could be wrong on a lot of this)