If your budget is limited, and the choice would be, do I buy a piccolo or do I take flute lessons, then I would take lessons.
If you are already studying with a really good teacher, then do pick up the piccolo! But your chances of getting accepted to a good university are pretty low if you haven't been taking lessons for at least two or three years. Simply playing in a high-school wind ensemble (even if you're first chair) won't prepare you for university-level work.
Definitely start lessons with a good teacher if you don't already, and yes piccolo will help!
And no piccolo will not be required in auditions but I did play picc for 2 of my three college auditions.. One I brought it completely unknowing whether she'd want to hear it or not, the other one I knew said definitely play piccolo if you can though that was for scholarships not really acceptance.. but in their top ensemble EVERY flute player is required to also know piccolo as they rotate piccolo, not just give it to the first stand.
Either way piccolo is kinda fun (or at least i really like it) and is also kinda challenging and will help your music ability and flute playing even if you don't play it for auditions. Id definitely start playing it if you can