Not sure if charging while off would extend battery life...but it does charge the battery much much faster while the phone is off. Full charge in about 1.5 hrs from empty if phone is off.
Since I use my phone as my alarm, I don't power off to charge at night. I just sometimes do it during the work day, to exercise/re-calibrate my phone's battery status apps...drain 100% and then fully charge 100%.
I actually disagree that charing it while off will "help extend battery"
The reason I disagree is that the charger provided with the phone will output a max current. If the phone is on, some of that current goes into power the phone, while the rest (minus some efficiency) goes into the batteries.
So if the phone is on, the battery will charge slower (and this also makes sense)
Now, most people know that charging a battery quickly is bad for the battery. If you charge a battery too fast, it can heat up past a safe point - which will doubtfully ruin the battery, but will surly decrease the batteries life-span (not charge, but overall 1-2 year lifespan)
It makes more sense to charge the battery slowly, allowing the chemicals inside to react in a slow, stable way
I turn my off and charge. 100% when I boot up. Leave it charging overnight while on and the phone cuts off from the wall charge when full and switches to battery. Want to start the day with a full charge.
i noticed that this is sorta true.....when i charge it overnight while its off, it takes a bit longer for it to go from 100% to 99% once I unplug and use the phone. But once it does drop to 99%, the battery drain/battery life is back to normal. So I guess it does extend the life a bit but not a huge improvement.