Hi Aaron,
The job is a cool one, though the hours can be long and the pressure intense.
A network systems admin connotes both system and network responsibilities. In general, you'll see mediocre skills in one area coupled with very good skills in the other. A great NT or Unix systems admin will know enough about networking to keep things working, and is often pressed into service as a network admin. A true network expert will have knowledge of the various protocols and how they are impacted by the network infrastructure.
I've been a systems admin and a network engineer. I find that it takes a great deal of education to be hired as a network engineer, but very little to have it thrust upon you. Case in point: Let it be known that you can assist the existing network engineer in setting up or verifying the firewall and the firewall rules and you will eventually be considered his/her backup and maybe his replacement. Same goes for understanding any of the gateway routing protocols.
The hours can be long because so much of the work has to be done when it does not impact your co-workers. This encourages late hours and midnight installation parties. The pressure can be high simply because if you screw up, everyone knows. Think about it. If your boss blows the budget, it may go un-noticed. If you blow away the file server with 5 years worth of data, everyone knows. It does not seem to matter that you have backups and can restore all the data.
The pay ranges from stinking to great. The market is over saturated in the US by foreign workers brought in under 401B visas(short term, specific job visa), who then had families here have stayed as general immigrants.
A great deal of system and network admin can be done remotely. Some admins have managed systems that they have never even seen. I've administered a dozen systems for the last 5 years from an office 50 miles away. There were several that I never saw after building/configuring them and shipping them to the data center.
My education? Completed high school and then supplemented that with 30 years of on the job training, technical classes, college courses and reading. I have enough college credits to get a bachelor's but not in the right areas (not enough general ed). The field changes enough that I expect to continue training for the rest of my career.
Daniel