It 'll work, it depend of your material. First, ask the power of your spindle. Generally, the power of air spindle is very low (25-100W). If the cutting power is bigger than the spindle power, the spindle stop.
You have a lot of litterature how to calculate the cutting power.
Personnaly, I use this air spindle.
http://www.nsk-nakanishi.co.jp/en/in...s/imf/hts.html
It works very vell, with very small tool diameter <0.5mm...