Yes, one can normally see Google ads on some song downloading websites, those sites are not using own song to download but pirated one. This is the issue for disabling AdSense when they get caught. The second one is, there is no issue in showing Ads in original (or own) song publishing sites (like official website or authorized website with copyright etc.).
Most of the audio and video owners nowadays are releasing and publishing their audio and video via online source only thus there is no issue if those websites are displaying Google Ad as long as the site abide by the terms and condition of the Google, whereas, few sites just releasing / publishing audio / video of other's copyrighted one which is a violation.