Now that our entire site is HTTPS, there does not seem to be any negative impact to our URL's by leaving off the HTTP protocol. If there was any traffic lost, it didn't seem significant as our reports did not indicate a decline. One year later, traffic through SEO is higher than before we implemented.
I personally agree with Everett, don't leave things to chance. I did require that the homepage did have HTTPS for the canonical though. I felt massive panic attacks while we were going through the transition. However, if you are unable to convince your developers the importance of using an absolute path for canonical this did not seem to have a negative impact on our site.
I am glad that we didn't have any noticeable impact, but I am also glad that I didn't turn it into a bigger issue within our leadership team. Since we didn't see anything negative, it could've reduced my credibility within the business which would've had made it difficult for larger SEO problems.
BTW, we are still using relative canonical tags today. (except the homepage, that still has HTTPS)