Yes it is possible for a socialist to be a successful businessman.
First, he can be a crony capitalist, getting funds and monopoly power from the state.
Second, he can be a hypocrite - socialism for thee, but not for me (i.e. “What I have is mine - what you have we share...”)
We already know about the crony capitalists, but a good example of the hypocritical successful businessman is Armand Hammer (Arm and Hammer products), who was a Soviet agent of influence for most of his life.
“What do you think the Russians talk about in their councils of state, Karl Marx? They get out their linear programming charts, statistical decision theories, minimax solutions, and compute the price-cost probabilities of their transactions and investments, just like we do.” - Arthur Jensen (Network)