When I learned arc welding, we had to perform overhead welding and some slag does fall onto your helmet and faceshield; however, it reduces with skill.
Molten metal rapidly solidifies because of the chilling effect of the parts being welding, if not, then the overhead welds would look ugly. Sometimes, we add chill bars on thin pieces if not quick enough and reduce the heat affected zone and sometimes we watch our interpass temperature (using tempilstik) if it chills to quick (thick pieces) which will crack the weld.
If the welder is qualified, you wouldn't be able to tell if the weld was done flat, vertical, or overhead.
It will fall for sure if you do not know how to.
You need to monitor how big your melt is.
And control your current and welding technique steps well. It is a permanent challenge with gravity. A game between cohesion forces of the molten parts and gravity.
Look at this: You can stick a drop of water hanging under a table, or attach that much paint underneath too. When you make the quantity or size bigger, it drops.
And when you weld overhead make sure you are well protected, because the drops burn deep.
The choice of electrodes can give you some advantage too.
Overhead welding is the most difficult position in welding. Not only do you have to contend with the force of gravity but the majority of the time you also have to assume an awkward stance. Nevertheless, with practice it is possible to make welds equal to those made in the other positions.Welding Equipment