Absolutely; for sure. The idea that something is so definitely true that you can wager your life on it originated in nineteenth-century America. The San Francisco Sun Dispatch used it in 1852: “He’s around when there’s money . . . bet your life on that.” Other versions are you can bet your bottom dollar, referring to the last of a pile of them, and you can bet your boots (also a valuable item), both of nineteenth-century American provenance, and you bet your (sweet) bippy, a euphemism for you bet your (sweet) ass, which was “bipped” out on television programs. The last two are both mid-twentieth-century Americanisms.