Well it won't turn everybody, but you'd still see some growth. And it generally works better with the 1000s to 1600 or 1700 era, as the Ottoman Empire and the Mughal Empire can generally prove. There were a great many people who converted in order to reach the upper echelons of government, and should this Jewish state do something similar, it's an effect which could happen.
Well, I'm trying to imagine why you'd need to convert to reach the upper echelons of government. As opposed to the House of Solomon(?) accepting loyal governors of whatever creed.