Yes, that's exactly the reason to backup in iTunes.
Since you are not currently jailbroken iTunes should offer you the choice to either upgrade or restore the firmware.
Upgrade, does as you might expect, and applies over the top of your current setup. This has been known to cause users a few issues if you are upgrading between major iOS version - e.g. 3.x to 4.x. In that scenario I would not recommend it.
The restore option will put a factory fresh copy of the latest firmware on you iPad, 4.3.3 in this case. Then, when it is complete and connected back to iTunes for the first time, it will ask you if you want to either set up the iPad as new, or restore from a previous backup. You must restore from a previous backup to get your settings back, including Angry Birds scores! When that restore is completed though, you MUST allow the iPad to reboot (without disconnecting it from iTunes) and then sync all your apps back on. Otherwise none of your Apps, including Angry Birds, will actually be installed.
So, in summary it sounds to me like you should be doing.
1. Sync in iTunes to take a current backup.
2. Restore the iPad to 4.3.3 (automatic since it is the latest version)
3. When connected to iTunes for the first time after restore, choose "restore from a previous backup"
4. Let the iPad reboot and fully sync so that all your Apps and Settings are restored.
5 Jailbreak - I suggest you follow the redsn0w tutorial which is a sticky in this section.
Hope that helps.