Oh yes. Burger is a different beast than chicken to be sure, but wood smoke is curative, and cooked food lasts longer in general. I've had cooked burgers in a trunk/backpack for up to three days, hiking and the like, in the summer, that didn't go bad. I bet if you cooked it, you could pack it in a jar with vinegar right away and it would stay good indefinitely.

Or if you expose it to smoke long enough it cures it completely and doesn't have to be refrigerated at all forever. Usually salt is involved, and often other plants that help preserve it if traditional curing. If new age curing they use toxic chemicals like sodium nitrates to cure it, like in ham or bacon nowadays. Those are to be avoided and are bad for you, just as preservatives like sodium benzoate put in condiments and the like, even in some pop, is bad.

Personally I always sprinkle some yellow 5 on my food after I cook it because testicle shrinking properties or no, it's worth it to not have to eat food that's not yellow enough, yuck.