"No EU Commissioner has to have ever stood for election, or indeed have ever been elected for any public office before being appointed as an EU Commissioner."

I googled the first 4 commissioners I came to including Juncker himself and all had previously either been elected members of the European Parliament or elected members of their own national parliaments. So yes and no. They don't need to stand as commissioners an won't be serving elected members anywhere at the time they are appointed by their respective governments for the post. Not ideal but kept in perspective the EU has 28 unelected appointed members in the commission at anytime - the UK currently has many hundreds of unelected members in parliament. Some aren't even appointed as they are hereditary. We have an unelected Head of State. And prior to his resignation the UK had one appointed unelected member of the commission - but at the same time we had two unelected appointed members of the Cabinet in Baroness Anelay and Baroness Stowel.