I am not going to discouraging u. Truly say, a good company doesn't consider the experience of faculty. Cause, in this field, u have to teach a particular curriculum and the training institute generally provides u course content or course structure which is really monotonous and u never do anything out of their course. So u got a very little experience, which might be no value. But in a company, ur work is not under limitations, there r no of various problems and u have to solve that. I am also working as a System Administrator and from my experience I told u. Before join, I also worked as a faculty in a renowned training institution, but my experience had not so value. If possible u will join in a company (may be it is not so renowned or very small) to gather ur experience.
And the current scenario is like that u have to join to a institute, then try at least join as System related jobs. Of course, if u will get chance to join in a National institute or like that, then u r on the right way !
Any experience you get, whether its as a faculty member of an educational institution or of a major corporation, is good so long as you are using and sharpening and building your skill-set.
Many colleges DO have multiple users, and therefore require good networking to allow their students to be online ALL at the same time. Supporting, configuring and trouble-shooting these types of networks is invaluable experience...