Unless you think your main filter isnt sufficient for the size of tank you have, if your tank is underfiltered ie. the filter you are useing is to small, then an airstone may be helpful, but if your filter is the correct one for your tank you shouldnt need one.
How big is your tank, and what make and model of filter are you useing?
And is your tank stocked correctly for its size, are you overstocked?
And is your tank cycled?
Anyway neons are not renowned as a hardy fish.
But if you give the above information it would be helpful.
Its not really the bubbles coming from an airstone that will aerate the water, it is really the surface turbulance and circulation that they create, surface turbulance increases the aeration/oxygenation of the water, but if your main filter has proper circulation of the water in the first place the water will rise to the surface and interact with the air and oxygenate.
And in planted aquariums airstones are auctually undesireable as they cause more co2 that plants rely on to be lost from the water.