Network above your pay-grade, these people are more interesting. Colleagues are useless.
However, a group of peers provides the following benefits:
* support and camaraderie, as you are likely facing the same challenges at the same times
* a more natural connection and more conducive environment for meeting and regularly interacting
* a rising tide that raises the whole group, as you help each other gain more success
Finally, I would say that your idea comes dangerously close to the idea of "kissing up and kicking down," which I personally find to be an unfortunate and disingenuous style of network management that discourages me from working with that person.
I've gotten jobs through former co-workers who have moved on to new companies. Some of my peers have been promoted into management and having a good relationship with them prior has given me a leg up. It's so incredibly easy to network with your colleagues. Just work hard and be a decent person and the network will create itself. Acting so dismissive of colleagues is short-sighted and silly.
I was talking about actual business opportunities. Good luck getting anywhere by being friendly to the, quick frankly, annoyingly arrogant sysadmin. Sure, some of them are nice - although most of them aren't because of the nature of the job, but that's not the point. We all are "nice" people, that does not pay the bills.