Presumably it does. Don't get me wrong, I don't think a white house ballroom is a good idea, or needed, or at all reasonable, especially when we're laying off what feels like entire scientific fields. Would I prefer a well-funded NASA? Yes 100%. The sticker price for the ballroom is a half of a space mission.
But the argument will be that it will help impress foreign leaders that have the same narcissistic tendencies as Trump. And this will overall be good for US foreign relations. Do I think that's a good argument? No, absolutely not. But it's one that can't entirely be ignored either.
I think even if it did somehow make it easier to schmooze with foreign heads of state, the real issue is that a whitehouse ballroom is anti-American. It is exactly the kind of aristocratic thing that America was founded to do away with. I can imagine some old king arguing that the royal ballroom is needed so that deals could be made with neighboring kings to avoid war or somesuch, and this is used to perpetuate an upper aristocratic class. America was supposed to have a government that was of and for the people, and there is nothing about a ballroom that fits that description. So even if it's advantageous in some form or another, even if you could argue that it will help get deals done and even foster peace, America is supposed to be about all of us being equal.
Trump's administration, even if you pretend that it's somehow effective, even if you pretend that it's somehow beneficial for all (which I do not think), is about elevating himself and those around him above the rest of the country. It's about being unequal. And that's fundamentally unamerican.