Yes, you can run Call Accounting Mate on your corporate server.
The reason why most PABX vendors do not encourage running call accounting software on the server is because they are not familiar with the Server. Therefore, they will sell you dedicated hardware specially for call accounting purposes. However, this is expensive and a waste of machine power.
Since Call Accounting Mate is a web-based system, there really is no reason not to install it on the server. You can just install Call Accounting Mate on the server, configure it using any browser on the network and off you go.