If one is particularly well-qualified according to LinkedIn, is it at all appropriate to include that point somewhere in the cover letter?
I would say no. It is understandable that such a statistic may sound interesting and worth mentioning, but nevertheless it was calculated by LinkedIn (some algorithm) and not the actual company or recruiter that is looking to hire.
It is true that Machine Learning is useful in those sort of tasks and analysis, and that it has been improving considerably in the last years (FWIW, my field of study is ML). Even though I am really positive that candidate matching could be feasible to achieve with good accuracy, it is a task that most humans are not quite ready to delegate yet.
Companies like to see, and talk, and come to really know their candidates before hiring them. Most companies have customized and sometimes long hiring processes for this reason.
That's why including that information in your cover letter may not help you much, as you would do better focusing on other things, like why should they hire you and what you know and can bring to the table.