You can airbrush on top of polish, but I've only ever done it when it's completely dry. Usually on myself when I get bored with the colour I'm waring! :lol:
To be honest I wouldn't recommend trying to airbrush over newly applied polish when you want to use stencils, for the reasons that you gave yourself.
However, if your clients request a "solid colour" underneath the design, you can quite easily airbrush the solid colour on first. Not only that but by mixing your paints you can even customise the colour for your client. Sky's the limit!
Because your "solid colour" is airbrushed on, it's immediately dry ready to add on a design, whether it be with stencils, colour fades etc. No worries!
But your client wants "her" specific nail colour??
Mix one up to match it. I highly recommend that you get a colour wheel, which will help you to understand which colours are needed to create a particular colour.
Yes, when you first airbrush the "solid colour" on it will look very dull, but as soon as you have sealed and top coated, the colours will come out beautifully.
I hope this answers your question.