Yesterday I showed my grandparents an iPad mini for the first time, and because the orientation wasn't right, they shook it violently a few times hoping that it'd orient it correctly again. I may be a bit paranoid, but is that going to damage its orientation hardware? What does the iPad orientation hardware look like?
The iPad Mini's accelerometer is a solid-state (with a microscopic mechanical - thanks Graham Parks for the correction) device so shaking should not hurt it. Electric shocks (for e.g. immersing iPad in water while it's on) and heat do damage electronics.
You're more likely to break the adhesive that connects the gorilla glass to the aluminium back before hurting the accelerometer.
Short answer: maybe. If you shake anything vigorous, yes, it will break. Will the actual accelerometer break? Probably not. You would have a connection come loose far before that happened, but that would stop it from working.
Here's the iPad teardown: http://www.ifixit.com/Teardown/iPad+Wi-Fi+Teardown/2183/2
Tell them to have some patience and all will be okay. Also consider this: your iPad accelerometer will work much better if you are holding the iPad perpendicular to the ground (up and down versus parallel to the ground.) With that, the accelerometer should do exactly what they want.