Don't pre-empt them on this kind of application, they'll be doing it for a reason (likely to minimise the amount of reading they need to do when screening candidates). If you start trying to give more than they asked for, it may either annoy them, confuse them, suggest you can't follow instructions, or simply be discarded.
Some people place far more emphasis on formal qualifications than the less specific information in a cover letter. Others the reverse. This organisation appears to place emphasis on qualifications and experience, so give them what they ask for. If they wanted a covering letter they would have asked for one.
I would consider adding a bit of a personal statement to your resume. Just a couple of short paragraphs, mine is about 8 lines total, as a kind of "sales pitch", similar to the "You have 30 seconds in a lift, sell yourself" idea. Don't go over the top, but it's a good place to add a few important words and mention things like communication skills.
Cover letters don't really achieve much other than when sending an unsolicited or blind application, in which case it acts as the introduction for the CV and yourself. In this case, they already know you're sending a CV, you don't need a letter attached to tell them.
With one exception
If you have specific circumstances you wish to mention, which you feel may mean your CV is thrown out early if not explained, it may be worth sending a covering letter anyway including details of this. I would only suggest this for that specific situation.