It sounds like pathfinder may be your friend here. Go to Effect > Pathfinder > Merge, that should give you the result you're looking for.
If there's any strokes in the art you'll need to expand them first (Object > Expand).
Since an engraving place is using the file you may want to make sure there aren't any extra paths in the file. After using the pathfinder, direct select one of the objects, then Select > Same > Fill color. Create a new layer and move the selection to that layer. Turn off the new layer and Command+Y to show wireframe. If you see anything where the logo was, delete it (it will probably have no fill).