I am Edgar Leeman from the Netherlands, descendent of the Swiss Othmar Leeman (died in 1807) and I have recently investigated my ancestors.
There is a Dutch seaman, Abraham Leeman, who is very interesting. He is born around 1620, so probably not directly related to your ancestor.
I also do not think that Abraham Leeman is directly related to me, but I do know of his existence.
He was Dutch. Abraham Leeman has discovered an Australian island, near the westcoast of Perth and there is a town named after him, Leeman. I have to apologize that I do not have all information at hand, but I believe that he was sailing on the "Vergulde Draeck", a ship that wrecked near the coast of Australia. Abraham spent some time on this so-called Rotten Island, survived and sailed to Indonesia on a float.