It depends on the item and the "local" option, but if I like the local option, then I will go out of my way to support it, and most especially: I won't go out of my way to get something cheaper elsewhere. An example would be book shopping, and for local I'll use the example of a Barnes and Noble(it's local enough, and we don't want it to pull a Borders). I *could* go to Barnes and Noble, and then order books online, which to me would be the most despicable option. I *could* just shop online in the first place, maybe even from Barnes and Noble's own website(thus getting the "cheaper" option while not supporting the local brick and mortar itself.... that still seems bad).
Or I could take my happy ass over to the bookstore, enjoy walking the aisles, and if anything strikes my fancy, buy it there.
I won't support local just for the sake of supporting local(I don't like buying anything in the first place), but if there's a shop worth supporting, and a product I like getting, yes, I'll support them.