Can the iPod touch work without a battery

No iPod Touches can show the battery percentage at the top of the screen (unless you jailbreak them). There are apps in the App Store that will show the battery percentage when you run them, but obviously not all the time.

There's a discussion thread here: http://forums.macrumors.com/showthread.php?t=1013295

• If you're using Windows, you're basically locked into using iTunes to manage your content; some people don't like iTunes.
• Syncing non-media content is weird, too. There isn't a unified sync system. I sync calendar via Google Calendar, notes via SimpleNote, and general files with Dropbox. Some apps only sync with your computer over WiFi, which is a hassle for me at work where the wireless network is not set to permit this. Sync is really important for the iPod Touch because it's nice to have a lot of your data at hand all the time, but it's a pain to type it in manually because it's so small.
• You can't easily update podcasts on the device. I couldn't sync for one week one time and had to update each episode by finding it in the iTunes store.
• It's really smooth, so if your hands are greasy it's easy to drop. Mine has handled drops well. I'm glad I use plastic screen protectors, though.

These are the most potent drawbacks I could come up with. I haven't found any comparable devices that solve these problems any better, though. Non-phone smart devices that fit in your pocket that aren't iPod Touches basically don't exist now; there are some Android devices in the works. I'm delighted by my iPod Touch and absolutely recommend the device.