Yes!  This theorem was proven by Moser using volume-preserving flows.  A manifold with a volume form is the same thing as a manifold with an atlas of charts modeled on the volume-preserving diffeomorphism pseudogroup.  He found an argument that can be adapted to either the symplectic case or the volume case.  I cited this result in [this paper][1], where I also established a similar result for the volume-preserving PL pseudogroup.

  [1]: http://front.math.ucdavis.edu/9504.5230