I'd agree with JMPC fully, you won't go beyond an entry level job in any IT field no matter what qualifications or technical certifications you have without hands-on experience.
I'm not 100% sure what an AS is (i'm based in the UK) but I can categorically say that unless it teaches you how to configure a Cisco router, Check Point firewall, or F5 ADC etc, then it's not going to be worth it. That's my own opinion of course, but as a network engineer, I wouldn't be picking your CV out of all the job applications if you didn't hold at least 1 entry level certificate from one vendor. Unless we had an opening for someone willing to do the crappy jobs :)
You could go the self taught route (as i did) and study an entry level industry qualification or pay the money and go for an instructor lead course. The former will be a lot slower the latter a bit quicker, although I would say it depends on your aptitude for the subject matter.
I would highly recommend, if you want to be a network engineer, that you start with the Cisco CCNA Routing & Switching qualification:
CCNA Routing and Switching - Cisco
There are other entry level certificates that you can go for, but the Cisco material not only covers Cisco equipment (which 99.9% of all networks will use in some fashion), but also covers network fundamentals which apply to 100% of all networks. Once you have that, I guarantee itwill get you a job working somewhere as an entry/junior level engineer.
Once you have completed that, you can start studying for further qualifications in networking that are relevant to your job role and/or interests like a security engineer, voice engineer, data centre engineer etc. to further your earning potential and career options.
From my own experience, experience will only get you so far nowadays. A lot of companies (especially in the UK) use agencies for hiring, and they are only interested in the certificates on your CV, rather than your actual abilities so certificates do open a lot more doors for you in the way of jobs, and the more (and 'higher') certs you have the better.