Hi Paul and welcome to the BrickWood forums.
Beautiful work on the base! I really love the way that stacked stone looks.
I think your instinct about what’s going to happen when your stonework goes from vertical to horizontal is correct. There’s another consideration: just as the firebrick underneath all have wide outer joints at the apex of the arch, so will the veneer.
I’ve flagged your post so that @BrickWood will see it; he’s seen just about every application of veneer there is. But my general opinion is that you would want to grout the arch for the reasons you mention.