Yes, he only meant that "story-wise", as in there is a lot of competition between hunters for Marks because of the rewards. You can leave the hunts for as long as you like. I remember one thread here recently from someone who was really far in the game and was finally going back to do the Gil Snapper hunt. He had the same concern as you, but he had no problems. Now that being said, obviously you have to complete some of the hunts before other ones can become available, but there are many others that become available simply from progessing further through the main storyline. So no worries about them disappearing.