No. It doesn't recognize the disc as being burnable.
You can burn them onto a DVD. Just make sure you buy the right type of DVD. Some will only burn to DVD-R and some only use DVD+R. This is particlarly true of older models.
You can get an external CD burner for $50 or less that will do the job. This is one:
24x10x24 CD-RW/8x DVD-ROM USB 2.0 Slim External Drive (Black)
A more immediate solution would be to transfer the songs to a USB flash drive and take them to Kinkos and use one of their computers to burn a CD.
Or just send the boyfriend the songs on a flash drive and let him burn a CD.