I have used craft acrylics without problems- at least no problems compared to model acrylics. One of the reasons I do not use acrylics more is the fast drying problem, which can be a disaster in both airbrushes and regular brushes. You must be very diligent about cleaning immediately, with either. Folks tell me to use retarder, but I often cannot find it. Only some hobby shops in area carry it, and I don't even know what to look for at the craft stores. It seems some model acrylics use different solvents/thinners than others, so it wouldn't surprise me if craft acrylics are the same way.
My understanding is that when we say acrylic paint, we are talking about the vehicle, and that vehicle can be mixed with different solvents. I have heard of acrylic lacquers, acrylic enamels, etc.