Mohammed was pretty rabid in opposing the idolatry of his time (where people worshipped the symbols of their gods), so much that he didn't want any symbol to represent Islam for fear of that happening with his religion. So, no, the crescent doesn't really represent Islam except for the fact that the Ottomans hijacked it from the Christians 800 years after Mohammed.
However screwed up Mohammed's implementation was, he did have a good goal: you and your god, and absolutely nothing in between.
People and a couple centuries, always seem to screw things up.