if 奥巴马 was a sentence in classical chinese, what would be its meaning?
Yes, if it is the way you interpret the characters, you can translate that into a sentence. However, you probably should not say this to an average Chinese user, it would not make any sense to them. Actually, if you would like to interpreted 奥巴马 to any Chinese sentence that makes some sense, it is nearly impossible. I personally do not see an modern Chinese sentence or often-used classical expression.

Firstly, one Chinese character could have many meanings. Here, all three characters have more than the meanings you have mentioned above. Thus you have a much bigger chance to find a sentence.

Secondly, it is less common in modern Chinese language to use one character for every single component of the sentence. So I would say the better way is to view the sentence the classical way. This has lead to another interesting point. The sentence pattern of classical Chinese are so different from the Chinese we are using now. Thus the chance of you to find a  sentence is even bigger.

Now I actually see a lot ways to interpreted 奥巴马 into a sentence. For example:

奥 - the Southwest corner of a room

巴 - to stick (v.)

马 - horse

Thus the sentence could mean "A horse is sticked at the Southwest corner of a room."