If I take a corned beef from the store and put it in the smoker, will it become pastrami?

If you smoked a corned beef you would end up with a very salty almost inedible piece of meat.

Pastrami is smoked after curing and usually uses a dry rub, corned beef is done in a brine.

If you wanted to try it I would soak the corned beef for a while in fresh water to remove some of the salt. Much like you would a Country Ham before you cook that.

you would have a rubberized but smoky corned beef.

Pastrami is also steamed.

No, since it has already been 'corned'. What you need is a Brisket of beef-not corned beef. It is sold fresh in most grocery stores.