Hi, Willwall -
First, welcome to the forum!
Second, I've moved your question to it's own thread for two reasons: (1) So it won't be buried in a conversation and more eyes can see it and (2) it's considered bad manners to "hijack" a post with your own, off-topic question (not to mention that it's against the forum's rules!). If you have a question, go ahead and open a thread of your own. It helps keep the boards nice and neat...
For your question, AFAIK, yes, the app data is backed up in iTunes. You should be able to transfer it from iTunes back to your iPad with no trouble.
But, my question to you is, did you try a re-boot of the iPad before uninstalling that app? Sometimes, the iPad needs to be taught who's boss. To reboot, just hold both the home and sleep buttons down until you see the Apple logo appear (the slide to unlock screen may or may not appear). Once you see the logo, you can release the buttons. After a bit, your iPad should appear as normal.
It's just that often, with unresponding apps, rebooting seems to solve the iPad's "wonky" behavior.
Good luck and let us know how you get on.
Marilyn