Connecting a Roku device to a Roku TV is absolutely possible (and possibly recommended), but it doesn't exactly "improve its reception and speed". It's similar to connecting any other device like a Blu-ray/DVD player. You switch the TV's input to the input of the Roku device and use the new device's remote to control it. If you only stream and don't use antenna channels, you can pretty much just have the TV power on to the Roku device's HDMI input and you may never need to use the TV's remote. If you do watch antenna TV, you'll have to switch back and forth with the TV's remote.
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