I was using Windows Server 2008 R2 as an OS. Anytime I would login to the VM directly, the soundcard was present.
After changing the settings in MSTSC (Microsoft Remote Desktop) to allow sound, I was still seeing the same issue. I have a feeling that this issue with because of the OS, not actually the system itself. I am currently attempting this with Windows XP, however I don't know if it will allow unlimited concurrent connections, or as many as we're going to need for that matter.