It would be ironic if I couldn't do this.
It's your personal matter if you slurp noodles or not.
Little Tokyo is in America. Despite the irony, slurping your food in America is pretty rude.
There's nothing little about Tokyo.
Yes you can. whether the other diners will consider you Gaigun/barbarian/uncouth/slob depends on rest of diners culture. Shanghai Chinese, Cantonese culture accepts the slurping as gesture of approval of taste of noodles. Japanese cultures vary from working class, salaryman class, student class. 'Little Tokyo' is common term for areas of Japanese tourist shops- which actual city are you referring to?