I was on an organized ride a couple months back and saw a guy on a recumbent with an iPad, so it's definitely possible. Worth it? Unlikely. The drawbacks have mostly been stated here, insufficient battery, possible flakey coverage due to connectivity issues, etc. I would also venture to say it would be tough to see the screen at times with full sun, especially if you have polarized sunglasses. I mean it depends on the bike your using and how badly you want the information, but if it were me, I would look at a Garmin Edge. This is a case where purpose-built devices are worth it.

By the way, I doubt the vibration would be an issue. There are no moving parts on a tablet (i.e. hard drives), so nothing there for vibration to hurt.