Gigabytes used when watching antenna tv

I don't know your exact setup, but I presume you are asking if you use an antenna vs Roku.

If you are streaming through the Roku, then you are using the internet through your internet provider or mobile provider, which will use data.  If you are using an antenna, then you are just using the airwaves that are provided over the air.

Keep in mind that a Roku stays connected to the Internet at all times, even when not being used as they may do updates when idle.