I cannot answer the question. I only use the part as an access point.

This depends on many factors and cannot be answered in general. Personally, however, I would not solve such a problem with this product, as the wifi reception is not very strong with this device.
If the TV box cannot be connected directly to the modem, I would buy another product recommended by your TV box provider.
E.g. Swisscom: Swisscom Wlan Connection Adapter Access Point Repeater or Swisscom Mystrom Powerline Starterkit 100mbits