having connections is a great thing. moral of the story is START NETWORKING!!! get to know people and be a decent likeable person and who knows you might just have someone offer to run your resume to the chief pilot.
The military connection is not just a way of getting all your friends hired... the military connection is there because military training has been proven over time. Its reliable, theres little room for fraud, and they generally wont fail out of training. This is by no way knocking civilian training which is usually excellent.
By the way this is a huge issue right now, a lot of guys failing out of training in the regionals... As an example, my friend at mainline AA showed me a thread on the APA forum and a memo from AMR was saying that sometimes up to 30-40% of guys arent making it through training at Eagle. So connections will only get you so far, then the rest is up to you.