i hope that your board has arrived by now. but to still answer your question: no there isn’t an emulator for a arduino boards as far as i know. mainly because there isn’t a need (if you have a board that is :-). the board is cheap and uploading a new sketch is as fast as it would be to start an emulator.
i admit that i wanted one to exist when i was waiting for my first board to arrive. but i don’t think i would have learned much from it. programming the board mostly isn’t the problem for beginners but designing stable circuits… how would an emulator handle setups that “work” but will burn your leds within a couple of minutes? after all i think arduino is about getting the logic out of you computer into the real world. a “real” emulator would probably be a nice thing to share and demonstrate designs over the web, but you’d need to be able to define external components and their behaviour which makes this a big big project.
hope you have fun with your board now. and welcome to the forum.