Current is not a feature of muck diving sites, but is sometimes present. Many muck subjects move about so don’t need current to provide nutrients.
Muck sticks are very much a personal decision. I typically do not carry one. I find them a struggle to manage and prefer to have both hands to manage my cameras gear.
What muck sticks should not be used for is: Subject rearrangement, as a substitute for poor buoyancy control and to try and get pictures in situations in which there is a possibility of damaging the environment. If a shot is proving difficult to get without impacting on the environment, move on....
I can normally shoot super macro without touching down however if there is a current, I would simply look for larger subjects