Some may consider it a technical and non-important distinction, but living together does not in itself establish a relationship which is qualified for sponsorship in the family class.
Cohabitation for a year is merely a minimal evidentiary element necessary to establish common-law. More than that is required. Being college roommates for multiple years, for example, does not a common-law relationship make.
The cohabitation must be pursuant to an exclusive conjugal relationship with a partner, a relationship with commitments on a par with formal or official marriage, and girlfriend/boyfriend does not make the grade.
Sure, many, many gloss over the details. Partnership sponsorship is perhaps the most common if not widespread form of immigration fraud. Anyone serious about establishing a life in Canada, however, should take pains to do it right, based on a legitimate ground supported in fact and intent. In the long run that is what works.
In the short run, it is indeed correct that the DUI looms as the obvious difficulty . . . but how flexible CIC's exercise of discretion will be, such as relative to whether a TRP is allowed, can very much depend on CIC's overall perception of the individuals involved, including the nature and level of commitment in the relationship. CIC cannot read minds. CIC can, however, make inferences and even if a couple can check off all the technical requirements for what appears to be a marriage in fact (called "common-law," in contrast to a "marriage-in-law" which is a formal or official marriage), if the circumstances suggest boyfriend/girlfriend rather than a commitment to a long-term marital relationship, how it goes in obtaining a TRP is, frankly, fairly easy to predict.
This looms particularly large in circumstances involving a coincidence between an impending loss of status and the somewhat recent development of a marital relationship (whether marriage or common-law), which is a circumstance that often triggers CIC's concerns if not outright suspicions about the genuineness of the relationship.
What is often overlooked is that once there is an issue, a problem, CIC's level of scrutiny and level of skepticism tend to increase across the full spectrum for the affected individual. It is not unlike the PIL officer at the POE, waiving traveler after traveler through, but then one little thing arouses a concern and that traveler ends up being questioned more thoroughly with a significant risk of a referral to secondary where the examination shifts gears, up a notch or three.
Always better to recognize bumps in the road before hitting them. And for bumps in the road toward status to live in Canada, that's when it is time to see a lawyer sooner rather than later, definitely before hitting the bump and finding one's case in the ditch.
