That's an odd theory. First I've heard of it. Why was Genesis 16:11-12 written, if he were just an individual wild man, then died? Who are the brethren he lived amongst?
What's an odd theory, that the Arabs were
not descended from Ishmael? The Bible says nothing about it. It was Muhammed, et al, who claimed this. The idea among Christians that the Arabs are the descendents of Ishmael has its origin among the Muslims. It has even less scriptural support than a pretribulation rapture. Some Christians especially love this part of the prophecy about Ishmael:
"He will be a wild donkey of a man;
his hand will be against everyone
and everyone's hand against him,
and he will live in hostility
toward [b] all his brothers."
They claim, well, it's true that this describes the Arabs so they must have descended from Ishmael. That, of course, is the fallacy of the undistributed middle: A is B and C is B so A must be C (or C must be derived from A), "Descendents of Ishmael will be troublesome and hostile, Arabs are troublesome and hostile; therefore descendents of Ishmael are Arabs." This is as true as saying, "Dogs are mammals. Cats are mammals. Therefore, dogs are cats."