Parallels is a single-user application in that one and only one user can use a particular VM at any one time. You can install multiple VM's on a particular machine, properly licensed, of course, and any single user can use any particular VM.
You can install a centrally located VM hdd file and have multiple users access it, but again, one at a time. You can probably even hack the pvs files to create multiple installs owned by mulitple users, but this is going to be so corruptible so fast it's not worth doing.
But ask yourself what you're trying to do. If you would like to have a Linux session running that multiple concurrent users can get to then yes, that is very possible with Parallels but thanks mostly to true multiuser Unix. To a lesser extent this is also true for Windows. This only requires a single installation of a Linux or Windows VM, and a single owner of the virtualization processes. Here's what sux about the whole process though...
Parallels (and independently, VMWare) have decided that the Mac version of their products are end-user oriented, meaning they are not intended to satisfy your requirement. The Parallels processes and the Fusion processes run as an end-user owned environment, and that end user owns everything to do with the virtual machine. That end user also has to be logged in to start them.
Accounts within any virtual machine can be created and accessed by any authorized users, but don't think for a moment this is anything like a true data center virtual machine environment where you have a true management console for managing multiple VM's. Multiple users can use the VM's to the degree that that VM's support multiple concurrent users (cya, Windows), but Parallels/Fusion are tied to a single user.
What would be cool is for Parallels/Fusion to run on a true Intel Mac server, launch from startup scripts, run as an admin-level VM manager account, and have concurrent VM's running using all available cores and apportioned RAM, and have a central management console to be used to control each VM. But that's not going to happen.