No, I'd start with Solitude or (when it becomes available) Winter Twilight first. But if by "rank beginner" you mean you've just found out where middle C is, you will need to wait for some weeks, maybe months before tackling them. The first few steps for you will be learning to read basic music notation and getting the fundamentals of hand independence down. That can take a frustratingly long time, and it's best to do it with material that's specifically designed for people new to piano.
You may want to start a thread on the teacher's forum to get their perspective on your second question. My sense is that teachers naturally prefer to have a student for the long term. However, I think most teachers would also agree that they'd much rather have a new beginner take lessons for three months and then quit, if necessary, than try to self-teach. The early weeks are very important for establishing proper posture and hand/arm movements etc.
p.s. By suggesting you wait on "Twinkle Twinkle," I'm answering from a pure logical perspective. However, if it's a piece that's captured your heart and you're just dying to learn it, a case could be made that--why the heck not?--just go ahead and work on it in addition to your regular material. There have been many threads debating the wisdom, or sheer folly, of working on pieces that are too advanced for one's level. I usually fall on the side that it's better to be enthusiastic about piano, so go ahead and work on dream pieces as long as you don't get too frustrated over the difficulty and as long as you recognize you probably won't be able to get it sounding like the original right away. Others disagree with that position and argue that once a piece is learned badly, it's extremely difficult to go back and learn it right later.
Edited by Monica K. (05/14/10 12:27 PM)
Edit Reason: added p.s. and fixed typo.