You can if your iPod classic is set to manual sync mode. You can then access content stored on the iPod through iTunes and have it output to the AppleTV via AirPlay. Of course, if you are going to use your computer for this, there is no need to plug your iPod in since all of your content should be in your iTunes library already (if not, you need to run out right now and buy a 250GB external hard drive for $35 and put your entire iTunes library in that as iPods should never, ever, ever be used as a permanent means of storing media).
You can't directly hook an iPod classic up to an AppleTV and there is absolutely no way to pass media stored onto it to an AppleTV without going through a computer.
