You can certainly run Mame32 from a CD, but it won't save high scores, control settings, any changes to Mame settings, etc unless you install the Mame executable to a hard drive somewhere.
I have Mame32 on a CD for playing at work. Our sysadmin is REALLY strict about having anything installed that we don't own, so I only install mame32.exe and the folders for hiscores, cfg, nvram etc to a network drive so it can write that data, store control settings etc. In Mame32, all the directories for roms, snap, marquees etc are set to the CDROM drive. Then I just pop in the CD any time I want to play, click the shortcut to Mame32 on my workstation, and it reads the copyrighted stuff (roms, snaps etc.) right off the CD!
BTW, I could never get the AdvanceCD to write to a CD properly. It needs a bit of set up to get going, so it's not exactly plug'n'play. Definitely not for noobs. Plus, since it's basically a Linux

boot CD, you have to reboot just for a quick game...