Yes if the probem was due to a defect in the iPod. Accidental damage like cause by dropping the iPod or damage from a liquid like water is not covered by the warranty.
Apple's Limited Warranty for iPod excludes coverage for damage resulting from accident, liquid damage, disassembly, unauthorized service and unauthorized modifications. Please review the warranty for further details. When a service is not covered under the warranty, Apple will return your original iPod to you without providing service, and may hold you responsible for shipping costs, plus any applicable sales tax.
An iPod that is ineligible for warranty service may be eligible for Out-of-Warranty (OOW) Service. For example, an iPod that has failed due to damage or liquid damage is ineligible for warranty service but eligible for OOW service. However, certain damage is ineligible for OOW service, including catastrophic damage, such as the device separating into multiple pieces, and inoperability caused by unauthorized modifications. Please see Apple's Repair Terms And Conditions for further details.
Note: There are Liquid Contact Indicators in iPod models manufactured after 2006. Please refer to this article to check if the Liquid Contact Indicator on your product has been triggered.