no, it shouldn't. i've never claimed warranty with Jetbeam, but i have claimed warranty with Nitecore, Fenix, iTP and soon Surefire (hopefully not), and none requires the "warranty card" (SF doesn't even provide one).
The s/n on the light is the ID of the light itself while the one on the card is related to the dealer you bought it from: the first two letters indicate in fact the country of the dealer.