Every company (or recruiter) is different. Some won't look at your resume without a cover letter, while others won't take a glance at the cover letter and go straight to the resume. I've worked alongside both types of recruiters. When possible, I tried to always read a cover letter. I felt that's where I was reading about the individual. It told me more of a story than the person. I got to see insight into how the person spoke (most pilots write as they would speak), how they view themselves as a professional and individual, and what they felt made a good pilot and fit for the company. I felt I saw more of what the person could bring to a company beyond simply flying an airplane, which anyone with a pulse and a license can do (well, for the most part). After a while I learned to tell who took the time to research the company or who simply threw our company name into a template created for 50 different operators. A cover letter is good for expanding on your experience that may not be immediately obvious to the recruiter. In your example, many recruiters may not know how a field like paramedicine would apply to aviation. They may dismiss such experience without a cover letter. I'll admit, I wouldn't have known until I came across my first experience with someone transferring from medicine to aviation, but that's why most operators have a recruiting team. A cover letter is used to sell yourself where your resume may not indicate relevant experience, so, yes, it can make a difference to those who view them. But you don't know who wants a cover letter or not, unless it is specifically asked for in the ad.
My advice is to always send one unless you're specifically asked not to. In the digital age, a recruiter can decide on their own to look or not. It takes a little more time for you, but it could be the part of the package that gets you the job.