Yup. The user might very well not live long enough to even get close to the battery.
Second question first: the resistance of an incandescent bulb depends very much on the filament temperature. It's much higher (resulting in a lower current limit) when the filament is hot, at the bulb's operating temperature. It's a lot lower when the bulb is cold/dark. This phenomenon means that an incandescent bulb draws a "surge" of current when it's first turned on; the current drops once the filament is at its operating temperature.
I measured a couple of incandescent and halogen bulbs in the 60-75 watt range, and got readings of 30-40 ohms. This means that a 60-watt bulb will allow around 3 amperes of current through, when it's cold and dark.
Compared to the body's resistance (hundreds to thousands of ohms, for a typical hand contact) the cold bulb's resistance might as well not be there. Almost all of the voltage will be developed across the body, very little across the bulb.
Even if the bulb's resistance was several times higher, and it were limiting the current flow to, say, a few hundred milliamperes, that's still ten times as much as is needed to induce ventricular fibrillation and cardiac arrest.
This "charger" is a deathtrap... it is an accident waiting to happen. There's a very good reason you do not see this sort of thing sold commercially.