Wouldn’t expect the bar itself to get hot; just the battery. The bar will be very low resistance and therefore only a tiny portion of the total heat will end up in it.
Now, if you stuck one terminal to one piercing and another terminal to another piercing, then you might have a bad time…
If you mean the bar, then even stainless of that size is going to be very low resistance - milliohms?
If you mean the body, then I believe it gets complicated. Skin resistance will be diminished by the piercings having a relatively large contact area and probably being somewhat sweat covered - I’m not sure exactly what the ‘skin’ inside the piercing tunnel is like. Certainly you can feel current from a 9V across the wet inner-body skin of your tongue.
The internal path will be quite low resistance because the inside of the body is a sack full of salty water.
It wouldn’t be fatal, even across the chest, but it could hurt.