To the best of my knowledge, Apple will not replace your broken screen and install a new one screen in your existing device. Depending on your purchase, they may replace the iPod touch with a brand new one, but they may also try to talk you into buying a new device if you voided the terms of their warranty from the event that damaged your screen.
I own the iPod touch screen replacement store milliamp.com, and I am certain that we can replace the screen on your 32GB iPod touch and get it shipped back to you quickly and it will look just like brand new.
We are reputable online repair store and have been in business for almost five years now.
Well, I hope that helps answer your question, and I will place a link below so you can learn more about our products and services.
P.S. Enter the code 'fullerhall' for a special Yahoo! Answers discount at checkout.
Anthony Magnabosco, Owner