Essentially, if you want to know about champions, you should read about them before or after meeting them in arena. Doing this while you are in the live arena is probably just a waste of time.
You also do not start a chess game and than read about rules how to operate your figures.
You encounter a new champion and lose because of the new one? Read about it afterwards to get more informed.
Taking reading time during the draft? You will more often be more angry about the automatic placement of your champ or annoyed because your opponent is really stretching the time.
I might sound rude here...but I don't want to waste time because the opponent does not know about champs and wastes my time to get informed about them.