Well, it should work, but I can't confirm anything because I've never had a pc without a soundcard.
If your CD-ROM Drive has any play/stop/next/prev buttons, then all you need to do is hold down Shift whilst inserting the CD. This will override autoplay, so no software will come up and try to play the cd.
If there aren't any buttons on your cd-drive then another option is to use the multimedia buttons on your keyboard. If you don't have a multimedia keyboard, then you need to find an alternative means of getting the cd to play.
You're in luck, because I also happen to be a moderator on the Winamp forums.
Assuming you're using Winamp 2x and not Winamp3
Install this Null Output plugin:
Null Output plugin by Vladimir Marko
This will make Winamp think it's playing through a soundcard
Now open Winamp, and go to:
Prefs (Ctrl+P) -> Plugins -> Output
Select Null Output to make it the active output plugin.
With the Audio CD in the drive and your headphones plugged in,
go to: Winamp -> Main Menu -> Play -> Audio CD
Voila!
Hope this works . . .
btw, there
might be a setting somewhere in WinXP which will let you play audio cd's without a soundcard, but I've not come across it yet. I'll keep you posted if I find anything.