I don't think it makes a difference as to the brand of TV. There really nothing special of the Sony HTC550W 3D sound . The fact is I don't even like mine. It only controls the sound bar, so you have to use the remote for whatever you plug into the sound bar or you wont hear a thing. Also there is a delay in the sound when you first select the device you are going to watch. If I had it to do all over again I definitely would not get a Sony.Get a Samsung.Also the remote sub woofer is not that great.
Yes, it will certainly connect via HDMI and would be an improvement over the internal TV speakers. Check with Mitsubishi and ask them about ARC (which of the three HDMI connections have this function). Keep in mind though that this Sony system is not surround sound and doesn't have a center channel. It is great stereo and simulated virtual surround with the remote woofer appropriately placed. If you are after real surround sound you will need to spend a lot more money on a higher-end system. My wife and I are very happy with the sound that we get from this system and do not ever plan to add surround sound down the road.