Hi ... just wondering - does spraying my indoor trees and plants do
anything for their health or is it purely to remove the dust and make
them look nice?

Probably closer to the latter.

Some plants like high humidity, but to really raise the humidity (a)
you need more frequent water than you will ever do by hand (see the
misters in some greenhouses), and (b) you'll get all kinds of molds
and such, unless they are in a greenhouse or other space without wood,
plaster, etc.

Many plants can be fertilized by spraying fertilizer dissolved in
water on them, but that's different than plain water.