Karl,
you want single engine VPs to go to fine pitch in case of pitch mechanism failure. Hence, a single acting prop will have the spring pushing the prop to fine and a dual-acting prop with flyweights will have the weights push the prop to fine.
That way, you can always fly at low airspeeds and have power available if the pitching fails. The only time this will do you in is if you are too far from a suitable place to land for the fuel to get you there at fine pitch. Getting stuck in coarse pitch could mean inability to produce enough power to remain airborne and would certainly hamper the ability to go around and/or climb.
In short, I do not know the answer to your question but I suspect that most single-engine VP props will be non-feathering. The philosophy being that if your engine quits, the propeller drag is usually an academic issue anyway and feathering ability would add complexity and be more likely to do you in than inability to feather.
Rgds,
/Fred