You do not need to run our system on a dedicated server. However we would advise that you monitor your server and check the general performance over time.
We have many small clients who run their AvaPA server on their office small business server which also runs their SQL and Exchange Server. It all depends on the size of your setup and the number of users who are going to be accessing the resources of your server.
One of our clients (Sandwell NHS Trust) run multiple versions of AvaPA (Nurses, Linguists etc) on a shared server.
We are happy to provide advice on a case by case basis.