In my view, it probably the opposite. Anchor in deeper water could drag easier as the chain in contact with the seabed became less. Thus, there is less holding force provided by chains. Hanging chains in water does produce much resistance.
Even for a very large contapinership, the weight if its anchor could be 10 or 11 metric tonnes (mt) only. The weight of each shackle of chain perhaps 20 tonnes (nobody onboard could tell me this). Therefore, there probably a total weight about 250 mt even with full length in contact with seabed.
A containship of 300m in length could have a displacement of over 100,000mt. At a speed of 2 knots, it has a momentum roughly 100,000 tm/s. The 250mt “anchor” probably has to be dragged a bit to fully stop the ship.