I've had multiple Palms. My T3 is still going strong, the wife uses it, and my old m515 serves as a backup PDA in case I ever have a problem with my TX. I get a couple of days use out of the battery between charges if I only use it for calendar, Bible reading, and other PIM/office tasks. I'd have to recharge it daily if I used it for video and audio. I keep the WiFi and Bluetooth off most of the time too.
My m515 is now 4-5 years old. If the battery is still fine on it, then I think the TX battery ought to last just as long. FWIW, there are some good 3rd party sources for replacement batteries.
Getting the extra warranty is up to you, but they're often just a profit center for the store and do little to help you once you actually need it.