Sync iPad 2 before upgrade iOS iTunes pops up a message and ask to sync iPad 2 before upgrade iOS to 4.3.3 due to there're purchased apps. After sync'ing, I only saw purchased apps in iTunes, not those free ones.

Does this mean, if I don't sync iPad 2 before upgrade, only purchased apps will be removed from my iPad 2?
Prior to upgrading, attempt the "transfer purchases" option in iTunes. With your iPad plugged in, go to "File" --> "Transfer Purchases from iPad". See if that transfers over your free applications as well. (I've had to do this sometimes to get all mine to transfer.) Note that this may take awhile to do.

Also note that this only transfers free applications from the app store, not built-in apps like the calendar, camera, etc.

And finally note that I've had occasions where even after I've transfered purchases multiple times, and can verify that everything did transfer correctly, that the upgrade process still insists that there are purchases that haven't been transferred. At that point, knowing I've done everything I can do, I ignore the warning and proceed with the upgrade. Probably won't happen to you, but something I've experienced in the past, so thought I'd pass it along.