The V6 does not need the network connection to record live programmes but EPG updates will not be possible if you turn off WiFi. I recommend connecting the V6 to the hub with an Ethernet cable (which will automatically disable the WiFi connection).
You've posted in the V6 board but referenced a TiVo - the two are very different boxes so check which you have - this page has pictures if you're not sure.
The TiVo has its own inbuilt modem, doesn't have WiFi or use your home broadband.
For the V6 - reference the answers you've been given. And indeed - relatives of mine who have a V6 recently went away for a fortnight and turned their homehub off. As a direct result, EPG updates weren't picked up and several series-links missed out on planned recordings.
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Thanks for taking the time to post in the forum in regards to the impact of turning your Wi-Fi off in relation to your TV services, welcome to the community.
As our VIP's have advised, there could (and most likely will) be some impacts if you were to turn off your wireless network. As the box uses the broadband connection for updates to numerous things (firmware, EPG, program changes) although the box will still record but as the guide may not be up to date it may be that the planned recording isn't what is actually recorded.
Is there a reason you are looking to turn the wireless network off whilst you are away? Is it just a safety precaution?
I've just realised that my post was misleading, so here it is with an amendment.
"The V6 does not need the network connection to record live programmes but EPG updates will not be possible if you turn off WiFi. I recommend connecting the V6 to the hub with an Ethernet cable (which will automatically disable the WiFi connection to the V6, thus enabling you to turn off the hub's WiFi)."