Nice try but no, the definition of "Shot" for a drink first attested in the 1670s, the more precise meaning "small drink of straight liquor".
http://www.etymonline.com/index.php?term=shot
While it's entirely possible the above story may have some truth it is not the origin of "Shot" as it pertains to the drinking of alcoholic beverages.
http://www.etymonline.com/index.php?term=shot
While it's entirely possible the above story may have some truth it is not the origin of "Shot" as it pertains to the drinking of alcoholic beverages.