The SuperDrive doesn't have a problem with MP3 CDs. MP3 is just an audio format.
It may have a problem with small CDs. In general, you should only put a small, round CD into a player designed for it ... such as a tray-loading player whose tray has indents for both large and small CDs. If a player is slot-loading, that's a big warning that using small discs in it will only end up in grief.
It sounds as though the disk you have is not so much a "MP3 CD" (a disk full of audio recordings) as a disk containing software that you need to use your new equipment. If you do not have a tray-loading CD/DVD-ROM drive that can safely accept the small software CD, you could try contacting the manufacturer, to see if they will put the software onto a full-size disk for you; or to see if they have it available for downloading on their Web site.
Another option might be to use Apple's software and/or third-party software to replicate the functions of the software on that CD, so you don't need to read the CD. Not knowing everything that it does and how it communicates with the hardware, I can't say if this is a viable option. Contacting the manufacturer to get a full-size CD/DVD or download might still be your best bet.