I suspect that except in dead calm oceans, doing this while heaved to (motionless) would be far more hazardous to currents, winds and waves, and would be impossible if it were anything other than a dead calm. Making headway would lessen that risk as the vessels can make adjustments to maintain formation that are simply not possible when stopped.
(NOTE: I was Aviation...never stood a bridge watch!) so others on this forum can correct me-I may be wet on this but I think I am somewhat on target here)
Tactically, in a condition of conflict or warfare, warships are slow in comparison to other forms of travel, and stopping to refuel is a waste of time...and lost time in warfare can result in loss of life or defeat in battle.
Stopped ships are torpedo magnets.