You still need to convince the IRCC that marriage is genuine. But yes, there are tradeoffs. I'm not advocating for any of these, I just believe it's very case specific.
I may be repeating myself, but if married, you generally don't need to show that the marriage is legally valid. (Well, all you do is show your marriage certificate, basically - the presumption is legally valid, usually).
For the common law test to be met, the cohabitation info - subject to interpretation - is a critical part of the evaluation.
Or put more simply: on a like for like basis (eg where cohabitation of more than a year), married is ALWAYS an easier app. Legal test met? Yep.* Evidence of relationship? Well, cohabitation.
Cases where eg attendance at the wedding is or may be crucial are for married-not-residing together cases, esp arranged marriages. Weaknesses of cohabitation evidence - including esp documentation of the start date - are not critical (arguably even important) to married cases.
Now this does NOT mean that everyone applying as common law must get married (although a bit less documentation). But for cases where the cohabitation period is short and/or there are other red flags - and especially documentation issues (to show cohabitation) - it may make the difference between more hassles and/or refusals. And yes - refusals I have seen here. We saw a few cases where the documentation of start of cohabitation was only a few days off - and refusal.
Rule of thumb that 'if in doubt, it will strengthen your case' is a good one. IMO.
*I could perhaps come up with some exceptions, but the ones I can think of off-hand are in the category of 'marriage not valid' (proxy, bigamy/previous marriages not demonstrated annulled/divorced, etc). Possible corner case - the few people who've had IRCC get confused by the handful of US states that don't have marriage certificates (but the courthouse stamps the marriage license), and that usually gets figured out. Suffice to say I think rare.