Can I use a fourth generation iPod Touch with AppleTV

NO. This

Apple TV: How to use AirPlay Mirroring

says:

To use AirPlay Mirroring, you will need the following:

• iPhone 4S (or later), iPad 2 (or later), iPad mini, or iPod touch (5th generation)1
• Apple TV (2nd or 3rd generation)2

However, some apps on or available for your iPod should support AirPlay to your Apple TV. See the section titled "If your device isn't using iOS 7" in this support article:

http://support.apple.com/kb/HT4437

Regards.