The escapement (the part that actually measures time) uses a spring and balance wheel so it will operate the same way no matter the presence or absence of linear acceleration in any direction. There is no pendulum or other form of eccentric mass involved in this part of the watch.
However, the self-winder is driven by an eccentric mass. It depends on the wearer's movement to turn it. A self-winder I had seemed to wind most efficiently in response to the natural back-and-forth movement of the wearer's arm while walking. It would also wind if held face-up and swung from side-to-side. What can be inferred from this is that the presence of gravity does nothing to help the self-winding action, and may inhibit it from working in some situations.
So, yes, any self-winding watch should work just fine in zero gravity, as long as it experiences some back-and forth movement.