Been in IT for almost almost 20 years (with a background in network engineering/security).
Network Engineering is under the umbrella of IT operation. As a whole, operations tends to key more on your experience than education. There are certainly places where a BA/BS will be required (e.g. Federal consulting), but it would rarely be accepted in lieu of experience.
Also, it's not really an entry level position. Many started in NOC/SOCs and/or helpdesk. Some went into system administration and 'transferred' over to network because they have a knack for it.
I'd also key in on this statement from your ECU link:
Quote:
Work experience is another area of emphasis in the Information and Computer Technology program. Students are presented with and encouraged to participate in various intern opportunities.
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I would ask a lot of questions regarding the internships that are offered. You definitely want to have a experience under your belt. Otherwise, you may end up spending a good amount of money on a bachelors, but still end up working in a NOC/SOC. Something you are probably qualified to do right now.
Bottom line - there is no certification or degree that is required be a network engineer. Do they help? Yes, they can. But experience is the trump card in this line of work. You can have a few IT certification and a B.S. and the guy who has 5 years of experience and nothing else will likely get the job over you.
That being said - once you have that experience, your degree will certainly come in handy when you start looking at management positions (should you want to go that route).