I only ask this because I mainly charge my phone while I'm driving (I have a 40 minute commute to and from work), so I use my home charger less often. But doesn't this automatically happen anyway? When I'm charging in the car, the screen does go dark without me having to do anything; wakes up as normal if I unlock it. I should observe what the phone does when I'm charging it at home...
Yes, your screen will timeout and go off if you do not do anything like hitting the power button.
it will do the same thing if you plug it in and leave it alone on the home charger as well, most of us just hit the button and set it down to charge. Doesn't really matter either way.