Once backed up iPhone to iCloud, can I delete an app and redownload it with same data?
As long as you don't make a single backup of your iOS device after you deleted angry birds, you can restore from a backup and the game should have data of progress you've made till the day of that backup. If you redownload the game, you would not have any app-data, regardless of anything, unless you've jailbroken your device and manually made a backup of the app-data, and reapplied it.