Will iPhone 4 turn on automatically when charging?
Yes, it will turn on once it reaches the minimum charge needed to start the phone.

When the battery is completely drained, you would just see a depleted battery icon (with a connect to charger prompt) for a few seconds if you press the Sleep/Wake button or the Home button. Once you connect it to the charger, it will charge for a few minutes and automatically start up, taking you to the lock screen.

At any time, you can wake your phone by pressing either the Sleep/Wake button (on top) or the Home button (below the touchscreen).