No, thats not what pulseaudio is.
A server doesn't necessarily mean many users on different computers accessing the same data on one server, a server is a program that handles many things at once. In this case, you may have many programs running at the same time, all of which interact at some level with the sound system -- ALSA.
Think of ALSA as the I/O handler that sits in front of the actual sound hardware. You have several applications sending and receiving their audio data to and from the sound server (pulseaudio). Pulseaudio then does advanced functions, like mixing multiple audio streams, adjusting levels, etc. before it sends the final stream to ALSA. Without this, it would only be possible for one program to be accessing your sound hardware at a time.
You definitely want pulseaudio to be installed on your laptop. In searching for the problem however, it may help to temporarily deactivate pulseaudio and set an audio program to communicate directly with alsa.