your old c drive is your main drive and you do not want to format it but boot from it, right?
your second drive is the additional drive and you want to format, right?
but the 2nd drive has an OS, right?
as long as you're not booting from the 2nd drive it's ok. just do what brian said and format it. just be sure that when you connect the drive go to bios and make sure that 2nd drive is not on the top of the boot order list. i'd personally not have it in there at all.
you can format it either way. i'd prefer to format it in your own pc and not the other as i can do on-the-fly last minute backups to the old c drive.