Echoing the observation posted by
@YVR123, just to be clear you are aware, there is not much point in contacting IRCC 65 days after making a PR card application to inquire as to the status of the application. And in regards to an application relying on H&C relief for failing to comply with the obligations of a PR, in particular, there really is no point at all contacting IRCC to inquire as to the status of the application at such an early stage of processing. Other than PR card applications meeting the low-complex criteria, IRCC often takes longer than the processing time posted for PR card applications.
But it is likely, in particular, that an application relying on H&C relief will take significantly longer (at least a number of weeks) than the routine processing time (an H&C application is inherently NOT routine), and could be considered high complex resulting in a referral to the Domestic Network for additional screening, which in turn can result in adding months to the timeline.
So, if you learn your application is approved in less than, say, three months or within 100 days of when it was made, sharing that information will indeed be appreciated. That will be a fair
indicator of what is possible. Of course it will not provide a reference for what any other PR can expect (other than, again, a reference to what could possibly happen) since H&C cases are so intensely fact-specific, how it goes being dependent on the particular circumstances in the individual PR's situation.
And, obviously, if in contrast you learn that rather than allowing H&C relief and approving the application, a 44(1) Report for inadmissibility is prepared, commencing the procedure for terminating your PR status due to the RO breach, sharing that information will also be appreciated . . . perhaps even more so because that seems unlikely (even though it is of course one of the possible ways this could go) and that would be an important illustration of what can be at stake for those who make a PR card application relying on H&C relief rather than following the conventional wisdom, which is to stay-and-wait until the PR has stayed long enough to be in RO compliance before making a PR card application.
Since you are only five months short of meeting the RO, and have submitted reasons supporting H&C relief, it seems unlikely your application will trigger the Report and inadmissibility proceedings, so other than expecting a longer than routine processing time line, the worst case scenario that is likely is a referral to the Domestic Network resulting in a four to six months, or somewhat longer, processing time . . . noting, again, that even though it seems unlikely, it is possible that IRCC proceeds with a 44(1) Report.
Good luck and please do return to update the forum about how this goes.