There can be a huge difference between what information is routinely shared between different government bodies versus what CAN BE and might be obtained regarding a specific individual through referrals and investigations based on specified grounds. Obviously, the upper limit of this is the use of full-blown warrants in criminal investigations, such as where IRCC identifies grounds to apprehend residency/presence fraud and makes a referral to the RCMP for a criminal investigation.
Privacy restrictions limit the extent to which information can be shared without cause. During the Harper government some of these privacy restrictions were trimmed pursuant to legislation explicitly expanding information sharing, particularly as between CBSA, CIC (now IRCC), CRA, and law enforcement.
The scope of what can be shared if there is CAUSE (grounds, reasons) ranges widely beyond what can be routinely shared. Cause trumps privacy to the extent of the government's articulated need for the information in a specific case. Again, the upper range in this is the full-blown, judicially issued criminal warrant, pursuant to which investigators can obtain in-depth access into an individual's government records. The "cause" must be particular to the individual, sufficient to justify the particular intrusion into the individual's privacy.
But the potential scope of this is, of course, huge, recognizing that if the government has sufficient reason the courts can issue warrants allowing a search of a person's home and the seizure of records and computer equipment and so on in the individual's home or office. Obviously, records held by other government bodies can likewise be the subject of a warrant. There is very little which is totally beyond the reach of a criminal investigation.
That end of the spectrum is a long, long way from routine inquiries conducted in the course of processing a citizenship application. This is NOT anything to have the slightest thought about, let alone worry about, for the qualified citizenship applicant who has provided truthful information.
But anyone who has submitted inconsistent information to different government bodies related to obtaining some government benefit (ranging from tax deductions to benefit payments, from credits to immigration or citizenship status) has reason to worry that one or other of the government bodies involved will identify reason to make further inquiries, conduct an investigation, and discover any false information submitted to one or the other government body. A lot of this, a lot of fraud, is done and not discovered. A lot of this that is done is discovered. The government provides secure housing, meals and bars on the windows are included, for the more egregious cases.
Address information generally:
In routine citizenship application processing there are many ways in which a processing agent can expand an inquiry to verify residential addresses provided by the applicant. Whether a processing agent does pursue any additional inquiry likely depends on whether something or the other triggers a question or concern. There are many indications that IRCC is increasingly accessing open source information, ranging from social media and Canada411, to online sites like LinkedIn, ordinary internet search engine queries, and it would be surprising if IRCC does not somewhat routinely at least glance at google maps, perhaps even in street view, to get an idea about some if not many declared addresses. Looking for incongruities.
Here too, the difference between what is routine versus what is done if IRCC has some suspicions about a particular applicant undoubtedly ranges widely. Routine: cursory look at applicant's information. Reason for suspicion: more in-depth review of information ranging up to a RCMP referral for investigation.
Additionally, it is now likely that GCMS records are kept for particular addresses, at least postal codes. We know for sure that there are GCMS records for some employers, those who have been identified as providing unreliable information in the past, or identified as associated with someone who has been involved in immigration, residency, or citizenship fraud. Thus, even in the routine application processing, a processing agent probably runs GCMS queries to see if there is a hit in the records against any address or employer declared by the applicant.
But again there are many approaches IRCC can take, and undoubtedly sometimes does take, to verify the applicant's address and employer information. Again, this undoubtedly ranges from cursory cross-checks for the vast majority of applicants, to intensely elevated scrutiny and even criminal investigations for those applicants who IRCC has suspicions regarding.
All this will be criteria-driven, fact-based, and rule governed. So it is not as if IRCC is at all likely to engage in unfounded fishing expeditions.
Apart from moral imperatives, there is a solid, practical reason for sticking to the truth in reporting information to the government: that is what works best most of the time. Those who do otherwise tend to get a stiff neck from always looking over their shoulders. Frankly, been there, done that, know the score, learned a lesson, paid the piper. Kind of like doubling down every hand playing black jack, sooner than later you go broke.