Can I restore data backed up from a newer version of iOS?

Unfortunately you cannot restore an iOS device to any backup that had been done from a newer version of iOS, using either iCloud or iTunes, due to the firmware. iTunes will give an error and iCloud will not even show the backup as an option to restore from.

To be able to use the backup that you have, you must upgrade the iPhone 4 to the newest 5.1.1 update that was just released. It should go smooth from there.

I work at the Genius Bar at an Apple Store.

It should be easy enough to set up the new iPhone 4 (temporarily), upgrade to iOS 5.1.1 (or whatever is a convenient latest version), and then restore from your backup to there, making your question moot.

I honestly don't know the answer to your question, nor do I have a way to test it to find the answer, but there's a straightforward workaround.