It is theoretically possible. (Theoretically. Nothing more.) The most consecutive heads I ever flipped was 13 (the card was Speed Stadium).
The "your opponent loses if s/he has no cards left in the deck" refers to the mandatory beginning-of-turn draw. In any other case, s/he would draw as much as was able. However, cards like TGW/Looker's/Claydol feed cards back into the deck, and this can happen late-game.