Perhaps the question is by on, what do you mean? You can either charge the phone while in full operating mode (i.e. home screen and apps running), or you can charge it while in "Charge only" mode. It is technically "on" during Charge only mode, but only on a very limited basis, just enough to activate the charging circuitry and charge monitoring circuitry as well as to provide visual representation of the charge level via a large battery with animated water-like level.
You can get to Charge only mode one of two ways. You can power down the phone FIRST, then plug in, or you can plug in and THEN power the phone down. Either way, you'll first have a full black screen and then shortly thereafter you'll see the familiar Red "M" logo. The difference here is, after the M logo, you'll see the large battery with the liquid level for about 10 seconds, then the screen goes black. It is NOW in Charge only mode.
You can check the charge level by briefly tapping the power button and releasing it quickly, then in about 3 seconds the display will light up and show the liquid level animation. Let it time out on its own. You can press the power button again to shut off the display but I've found it can sometimes trigger a full boot, just like tapping briefly to view the levels can. If that happens, once it's fully booted, hit the power button again and choose Power off. It will go black and then just as described above, first the Red M, then the animation again.