is the server really impossible to connect to even indirectly from outside your network?
That's the first question you should ask yourself. If the LAN can be accessed from a machine that has 2 network connections, one to that LAN and another to another network that is connected to the internet (hopefully through several layers of firewalls) you just connected that server to the internet.
And remember that a machine doesn't need to be connected to the internet for it to be vulnerable to attacks. A machine could be infected with malware that is simply intent on doing damage to it via a USB stick, floppy disk, or even typed in commands on a terminal.
In the end, all security, as all performance improvements, is a compromise. What's an acceptable level of risk for the rewards gained.
To find out your potential performance gains, run tests on the machine while it has no network connections at all and see for yourself. Most likely it won't be very much, but it might just be enough to squeeze out those few extra CPU cycles that help some old hardware survive just that bit longer that you have the time to convince upper management that you really, really, should get the budget for a new server.