Seriously....just get the passport! they only take a week usually to post out to you after lodging at the post office. You'll use it within the next 10 years (I assume you'll go overseas at some point in 10 years????)
I can't remember if I took my passport to recruitment day or not.....but......it seems a silly thing to be worrying about so just go and get it. One less thing to think about, surely?