HDMI on a soundbar (or receiver) allows the device to process all high end audio formats if the soundbar (or receiver) is capable. These capabilities vary by device.
A have a modest high end audio system that I use for music and a soundbar for video. My preference is for my devices to be connected to the television so that I may customize each video input for best picture. For instance, I use THX for Blu-Ray and DVD, one set of Custom settings for DVR, another set of Custom settings for PC and a third set of Custom settings for my wife's video camera. Finally I have another group of custom settings for digital photos. I then use either digital or analog outputs from each device to my soundbar for audio. My two primary components, Blu-Ray and DVR use optical which allows 5.1 audio. The remainder use 2-ch analog outputs from the TV as 2-ch is acceptable to me for anything from the PC or my wife's camcorder. No sound for my digital photos.
The CT-150 is a very good sounding unit and does have switching for up to three video components via HDMI. In such a system the only use for your Yamaha receiver would be as a possible tuner for the CT-150.