I say yes because of the simple fact that we are taller in the mornings than we are at night. This is because while we sleep, we relax and the tendons and ligaments that hold us together are looser and we can be as much as an eighth of an inch taller as a result. As we move about and things tighten up we lose that height. Also gravity and it's pull helps with that.
Now if you were hanging upside down, the weight of our bodies would stretch those tendons and ligaments and we would be a little taller as a result. However we would lose that rather quickly as we stand upright again and gravity does it's thing.
The "mostly no" part comes from the fact that hanging from the bar is not going to alter your skeletal structure in the slightest. It's not going to make the growth plates grow more than they're going to grow, they're not going to make them grow faster, it's not going to change the length of your bones...
So no. It's not going to make you any taller than you already are first thing in the morning.