It's splitting hairs, but the proof shows that for any finite bankroll (regardless of how large) it's an unwinnable system. If the bankroll is infinite (what I meant by unlimited, and presumably what the others meant), you can win any arbitrary amount you want, by expanding your bets by any ratio desired (i.e. triple after a loss). You're guaranteed to be ahead at some point, after which you can stop with whatever win you choose.
This does not, however, asymptote to a +EV for infinite trials.