I have a situation where a player chooses the Trader because it has 5 coins even though he has nothing to sell in the trading house. Can he do it?
Taken from the rules:
Implementing the action of a character is voluntary (exception: Captain)
Note: You can still choose Captain if you have no goods, the exception just means that if you pull Captain and have goods, you have to ship.
Choosing a role merely for it's privilege is a perfectly valid move. It may not always be wise to choose a role you cannot fully take advantage of but if you are really short on cash such a trade off may be warranted...