First, it is hard to justify "what is typical". Second, your mileage may vary.
Six discrete servers is way less than one tech unless you have extraordinary needs.
You should have plenty of time to handle 120 computers assuming you have spent some time getting things to work well in the first place.
We have two techs for around 200 PCs and a couple of dozen servers. As we virtualize the servers, we have even more "servers" but less hardware to look after.
Getting things to work well...
1. Can't get bogged down doing application work.
2. Remote control for all servers and workstations (huge time saver when we implemented this).
3. Build software to clone typical desktops so that rebuilds happen fast.
4. Automatic updates for virus and patches (all software). If you are still patching/upgrading software by walking around with a CD, you are wasting your time (although I've a lot of fun in the past doing that!).
5. Automatic backup. Get backup scheduled and running on its own. It should be in some form where you can be gone a couple of days and it still works. We have tape libraries and are moving to geographically mirrored data sets (still with tape backup).
If you only have one tech...I'd worry more about the "beer truck" problem (what if I walk out the front door of the hospital and a beer truck runs me over) than the workload. To me, I'd want some backup for you -- even if that person was "just" a PC tech.
BTW, I don't work on the network side anymore, but have good knowledge of some of the growing pains when I was more involved.
