The Kenwood amp is rated at 2Ω per channel so a 2Ω bridged load will create a 1Ω load
per channel. Since the amp cannot handle that load, it won't be twice as loud or cleaner but it will make the amp heat up to the point that the smoke will come out of it.
That said, the system will be louder and distortion probably won't be audible until the amp begins to seriously deteriorate but, technically, it won't be "cleaner". The reason it won't be twice as loud is that the power supply isn't capable of supplying enough voltage and current to the final amplifier in order to make double the power. What will happen is that voltage won't increase when it needs to and as a result, the final amplifier will draw more current, decrease efficiency (make heat) and ultimately, fail.
But yeah, you're right for the most part.