Do not go overboard with the cover letter. Make it a well edited 2-3 short paragraph letter that shows that you actually researched the company and you should be good. In life there are no absolutes so not all Recruiters/HR/Team leaders will read and value the cover letter but it will not go against you unless it is poorly constructed.
Also, if you have not been in the job world much you might not know that filling positions is not the most important thing that most of these people are doing so it is not really that high on their priority list. So what is needed is a phone call to the person telling them that you applied recently and was wondering if you had any questions about the resume. (This one might backfire sometimes but I think that it is a usual net win. The places that it might backfire at are usually places that you do not want to work at anyways.) They may have put you in a pile of possible contenders and if you want to differentiate yourself a personal call can show them that you are motivated and will follow through.
Also, if you have not been in the job world much you might not know that filling positions is not the most important thing that most of these people are doing so it is not really that high on their priority list. So what is needed is a phone call to the person telling them that you applied recently and was wondering if you had any questions about the resume. (This one might backfire sometimes but I think that it is a usual net win. The places that it might backfire at are usually places that you do not want to work at anyways.) They may have put you in a pile of possible contenders and if you want to differentiate yourself a personal call can show them that you are motivated and will follow through.