Yes, very slowly. You won't likely ever notice or detect movement in your life time, or the next two or so generations for that matter. In fact, unless something happened out of the ordinary within the nebula long ago, it should appear relatively the same from earth, for another 1000 years or so.
My sincere thanks to all the kind folks who answered my question regarding these nebulae.
Ver-r-r-ry Inter-r-r-r-resting!