How to make iPhone turned on after charging
In a word: Yes.  

To the best of my knowledge, the mere act of plugging-in the dead iPhone to a recognized charger will cause the phone to initiate the boot sequence once the battery has charged sufficiently to allow for running the phone and charging simultaneously.  

You can check this behavior by turning your phone off and then plugging it into a known-good charging system.  You should see the apple appear shortly and the phone will proceed to boot-up.