tom, no offense but you have not hit the job market yet so saying that your degree is getting you a foot in the door or this and that is kind of proving howies point.
you don’t know yet that it is going to get you the job… in many cases it WILL get you the interview, but networking will do that same task.
Why not put the argument to bed that anything is possible, if you want guarantees, get a degree, experience, and build your network.