Even if you start with $2 and go all in every bet @ 2.00 odds, after 19 bets you will be at $1,000,000. Or if you start with $500, it takes 9 all in bets to reach $1,000,000. It is possible.
Yes, you can achieve a similar result, but the percentage of winning 9 bets in a row is only 4%. If you start with $ 2, then the percentage of winning 19 bets in a row will be less than 1%. But the fact is that Archie Karas did not bet, he was playing poker and, accordingly, your doubling strategy cannot work.