They can. Objectives are legal zones. They will stop there as they cannot advance onto the deployment zones behind the objectives (or off the edge of the ships in the case of the expansion factions' layouts).
You may attack an objective you are standing on. If there is also an enemy Hero next to your deckhands, you would be able to choose between the Hero(es) or the objective as you prefer.
Then it looks like we played it correctly! Thanks!