When I worked as a full time recruiter at a corporate office where we were recruiting and filling positions nationally and worldwide we preferred not to receive cover letters. Rarely did we even give them a glance; we were too busy to read each and every cover letter. The resume was what mattered. Then after the resumes, the interviews made our biggest impression. The resume was what got our attention to pursue the applicant further for the position. Most of our resumes were submitted online, although we did get them in other ways occasionally. Unless the position was an upper level position (6 figures) cover letters were annoying and never given any time.
However, not all companies, corporate or not, are alike; there is a lot of subjectivity in the recruiting business, and in all business in their hiring practices.
If you submit a cover letter, and they don't require one (they will usually hint if they do or not in the job posting, but this is not always listed), the worst they will do it toss it aside, no big deal. But if you don't submit a cover letter and they do require one, that makes a poor impression from the start. To be on the safe side I would write a professional cover letter, just to be safe unless you know without a doubt they don't bother with them.
Your resume looks better, good luck with the position!
