Rather then talk. I’ll just show you how I did it.
Yes, it’s a solution. But now you have an invisible face inside the object, the top of your cylinder.
You could also select the lower edge loop of your half sphere. And then extrude it on the z-ax.
Good job!
Actually there is no hidden face in the cylinder. Every time I checked I couldn’t select it before I merged the two objects. But it really looks like it doesn’t it.