First of all, the answer to this can differ from state to state within the United States. In general, the answer is that it does not matter that the men were not armed.
The general rule is that a person may use self defense if they have a good reason to feel threatened. If a man wakes up in his own house, and sees two strangers walking towards him, he is certainly entitled to feel that he is in danger. Most states would not require him to determine exactly how dangerous the men were.
So long as there are no other circumstances that would have made it clear that the men were not a danger to him, the homeowner has the right to shoot them.
In any legal question such as this it is important to consider that all states vary about self defense. However in common law principles, the castle doctrine is the general rule. The basic tenant is that you have the right to stand your ground in your own home. A person is allowed to use deadly force to protect himself or members of his home. If the shooter himself was in reasonable apprehension that his or another's life was in danger, he has the right to protect himself and the others. That being said, there is no authorized use of force for the protection of property. If a man awakens in his home and finds a man exiting through the back door carrying out his television, he is almost certainly not in fear for anyone's life, therefore he would not be justified in shooting this person because they no longer represent a threat to his or anyone's life.