I was an apprentice at the Walnut about five years ago. As far as apprenticeships go, they really don't get any better than this one. For starters, you actually get a paycheck every week. But, even more importantly, if you're working on the mainstage, you'll be functioning as a primary ASM, and most of the time you--and probably one other apprentice on bigger musicals--will be responsible for running the backstage. In other words, you're truly an important member of the stage management team and not just "an intern."
Also, you'd be working alongside established professionals on Broadway-scale productions. And having the Walnut on your resume really doesn't hurt. My phone started ringing a lot more after working there.
The long and short of my answer is this: you should apply for the program and if you're accepted, you'd be a fool not to do it. I would be hard pressed to think of a better apprenticeship situation. Apart from working at a well-known theatre and learning a tremendous amount by actually DOING the job (and not having to do all those other "miscellaneous" jobs that interns are often expected to do), Philadelphia is an awesome town to live in.