Lobster is correct...some TV manufacturers make a TV with a Roku app. "A smart TV built for streaming Roku TV."
However, the TV manufacturers making the Roku TV are mediocre at best: Hisense, Hitachi, Insignia, Sharp, TCL. They're mediocre because their audio/video processing isn't very good. Their HD Picture Quality, Motion Blur, Sound Quality, Ultra HD Performance, Versatility and Viewing Angle all stink.
A TV should be much more than its apps. I advise choosing a TV based on its performance...not its apps. LG and Samsung are great choices, and Sony appears to be making a comeback.
Not considering its apps; choose a TV based on its size, picture quality, key features and all connectors you'll need for other equipment, such as a streaming media player, DVD player, game console, sound bar, Internet etc.
If a Roku TV happens to be one of your final choices, get the Roku TV. However, I'd highly doubt it would be because those TV sets are awful. Maybe a TV from Sharp could be a finalist. If a Roku TV doesn't make your list, you can always purchase a standalone Roku device (Stick or Player).
...but to answer your question, "will the Roku channels come in when the TV is connected to Cable box," the cable box will have nothing to do with your Roku channels. There would be no connection between the two sources.
If you want to switch from your cable box to Roku, you would only use the Input Select button on the remote control for your cable box. The Input Select button would instruct your TV to display all its connected sources: streaming media player, DVD player, game console, cable box, etc. From there, you would "arrow" to the Roku device. Then you'd use the remote for your Roku to navigate its program guide.
I'm unsure about the Roku TV; however, if you bought a Roku TV, you would probably use the TV button on the remote for your cable box to initiate it. For example, you'd press the TV button and then maybe the Select button to display the TV's menu. From there, you might be able to "arrow" to the Roku app, which would depend on how inclusive the code you used to program your TV. If not, then you'd use the remote for your TV to navigate.
Despite having owned "smart TVs" in the past which came equipped with built-in Netflix and/or Amazon Prime channels I've always felt most confident and secure in using dedicated streaming devices. My particular favorite being Roku. But this being America there are also other options, like Apple TV, Google ChromeCast and Amazon Fire products to name a few.
My personal reasoning is that I don't fully trust Sony, LG, Samsung, TCL, Vizio or any other manufacturer/marketer with my digital data, something most consumers overlook in their search for the ultimate, most convenient content delivery system.