If I buy a new iPod in an apple store, can I leave it there so they can engrave it?

No. Apple stores do not do the engraving.

If you want an iPad engraved by Apple, you have to order it from the online Apple Store. As lllaass said, you cannot get engraving done it a retail Apple Store. Some engraving shops can also do this, though many will shy away from engraving an electronic device, and you risk the warranty if you have someone other than Apple do the engraving.

I generally advise people not to get an iPod engraved unless you have a really good reason. Most people put an iPod in a case or skin anyway and hence will not ever see the message. In addition, engraving usually reduces the resale value of the iPod. So think very carefully before having your iPod engraved.

Regards.