You can certainly use Vallejo Model Color paint in an airbrush, it just needs to be thinned a bit more.
Exactly how much thinning, I can't tell you, as Vallejo paints vary in consistency considerably between different colours. I have some which are quite thin and some with the consistency of custard.
If airbrushing (or brush painting for that matter) a nice flat primer coat is recommended as they don't like to stick to styrene very well without it. I just use regular Tamiya acrylic as a base coat.