Depends entirely of how its set up from the get go.

Some places expect you to do everything from networking, user support, hw support. Pretty much everything.. Where you have to be a jack-of-all-trades to survive.

I'm lucky enough to have been, 8 years n and counting. At the same school district. In the beginning I was very much jack-of-all-trades, I had some linux knowledge, which was most than the other co-workers except for our sysadmin. Fastforward 5 years and here I am, in charge of most of the infrastructure (except for the network, we have a dedicated guy for that). But all the servers and such, sort of fell into my lap.

But as I said earlier, it very much depends on how your workplace is "configured", I've seen a lot of people come and go while the (well, they're double my age) call me for support.. I like my job a lot but do some serious research of how things work. If we were to get a new boss and I'm stuck at level 1 support all over again I'd bail the fuck out.

So.. TLDR: Do some research about how its all structured, ask questions (no one ever gets a stupid stamped in their face for being curios). I'd bail the fuck out if it turns out to be a very jack-of-all-trades line of work. If you're into sysadmin stuff, know your shit, it'll probably work out ok :)