is it "bad" for my new iPod if I do not use it?
Not likely.
Is the battery running out?
When bought on ebay, most likely it will be dead. Charge it for about 4 to 6 hours. After 5 to 15 minutes and the iPod doesn't turn on, then you need to get it replaced.
http://www.apple.com/batteries/replacements.html
Your one-year warranty includes replacement coverage for a defective battery. You can extend your coverage to two years from the date of your iPod purchase with the AppleCare Protection Plan for iPod. During the plan’s coverage period, Apple will replace the battery if it drops below 50% of its original capacity. If it is out of warranty, Apple offers a battery replacement for $49 (iPod shuffle), $59 (iPod nano and classic), $79 (iPod touch) plus $6.95 shipping, subject to local tax. Apple disposes of your battery in an environmentally friendly manner.
Should I use my new iPod right now?
Charge it first, after 5 to 15 minutes and it doesn't turn on, get the battery replaced.