It's actually nowhere near that, at least in the UK. (Disclaimer: I work in a school in the IT department).
The actual cost is based on the number of full-time *staff*, not pupils, and the rates are far lower than the $1000/year you quote. This gets you Office, Windows, all the CALs you need, SCCM and lots more besides. You still have to pay for server licences (Windows and SQL), but they're deeply discounted.
I don't know what it's like in the States, but in the UK school sysadmins (or network managers, to give them their more usual titles) will be on salaries of around £16K to £30K - or $27K to $50K, more biased towards the low end rather than the high end of the wage bracket. Or, at least, that's the going rate down here in the far SE of England. In our case, that involves using VMWare products, such as vSphere and ESXi, in addition to the various Windows servers.
NB, I got into this by playing games, as an earlier poster mentioned - it's a common thing to use Windows at home for games, as I did over 20 years ago, then start networking PCs, move on to running a home server or using server products on a home PC and so on. I made the jump with Windows 2000 (when I was at Uni), as Microsoft kindly sent out CDs of their server products to anyone who asked. Yes, they only lasted for 180 days unless you tinkered with registry files, but it was enough to ignite the spark. These days of course pupils and students get the full thing from Dreamspark.
I don't have an MSCE. Never saw the point of them, I prefer academic qualifications as it shows you're capable of learning anything rather than a specific method of one vendor's products. I'd never rule out a move to Linux, but for now our Microsoft-based network is serving us well.