IMO all that will happen is huge mess and it looks brass already

I have spray painted our outdoor light fixtures and storm door to match new porch lights. (I went from bronze to black.) The Rustoleum hammered metal finishes are very forgiving because they create a rougher texture.

I doubt you can get a mirror like polished brass in a spray but could get an antique brass look. All the little rods would be hard to clean for prep and spraying.

So yes it is possible but might be be more trouble than it is worth.

Yes, you need to tape off EVERYTHING that you don't want painted.

it's a slow process, but do it right, the first time.

Primer, then finish.