I can't imagine that inhaling salt would help with any health condition.

BUT natural salt - like sea salt and himalayan salt have been known to produce an ionising affect when heated/dissolved in water etc. Ionisation is when the air becames charged with a higher number of negative not positive particles, and helps the air to be fresh and clean - like it is when you're at the beach or standing next to a waterfall. This is the principle behind salt lamps which are fairly popular these days.

Holistically you could incorporate some of this into your LO's routine by using sea salt or himalayan salt baths (I used this a lot during my cancer treatment, it helps enormously with creating energetic balance), but I suspect in order to get a really good result, actually getting a room ioniser with a HEPA filter would improve the air quality inside the house most and provide the most benefit. Just my thoughts...

ETA thought I should add that ionisers actually cause dirty particles like dust, smoke, etc to fall out of the air, so expect to do more vaccuuming in the room you're using it in.