I think you have to have defined roles and tasks. If the call volume is low the Help Desk staff might be able to do backups and replace printer paper, but do you really want a Help Desk person building a production server or installing a network switch?

If you are small enough then a single person might be able to do both the Network and Systems Admin functions but eventually you are correct and will need two people. I suspect upper management is counting you as engineering staff when you should be managing the network and your systems. So I say maybe compromise and get one person now who can wear two hats.