Yes you can use cut vinyl when exposing screens - you can use a number of things but I still use clear acetates printed with a laser printer.

I used to do work for a guy who supplied his own print ready artwork and that's what it was - black sign vinyl cut on a plotter and weeded. The end results weren't as good as a posi due to the plotter not cutting perfectly, and also the thickness of the vinyl effected the exposure - but it does work. For very short runs of plastisol you'll get away with applying the vinyl to the screen direct, no exposure needed.