Fighting a fish while on the "hook" in a hog line is not only bad form it could also lead to bodily injury!! Those big floats you see on the anchor line are there so you can throw your anchor line over and drift with the fish and then run back up and reclaim your anchor and your spot. Make sure your float and trailing line don't hang back behind the other boats too far.
P.S. If you haven't had much experience anchoring in crowded conditions you should bring plenty of beer!!!!!!!