Yes. Here is a step-by-step tutorial – http://www.iconosites.com/blog/2011/11/add-music-to-your-website-for-free-iconosites-website-builder/
Note: If you go to www.podsnack.com you can create your music player (with your own choices of music), and then copy & paste the code they provide into the WSYWIG (you must use the HTML button when you do this) of your IconoSites website.
If you would like the music to play on every page of your website, then you will need to paste the code into the WSYWIG of the Footer, which can be found in the HEADER & FOOTER section of the admin panel. However, if you only want to the music to play on a single page (such as your home page), you would just cut & paste the code into the WSYWIG on THAT PAGE ONLY.