The question about whether zombies can use Allomancy really depends on the "zombie canon" you follow, as was said before. For example, in The Walking Dead, only the brain stem is active. The vast majority of zombies can pretty much only move, kill, and eat, though a couple of them have been observed to remember how to use primitive tools like rocks, and can attempt to climb over obstacles given enough time. My guess is that even if the instinct to use Allomancy remains (provided they even can, since in this particular example canon, the soul is absent by this point), they wouldn't have the cognitive processes necessary to apply it very well. Remember that even before Vin knew she was an Allomancer and was using her "Luck," she knew she was doing something and was applying it logically to her situation.
Zombie Thugs, however, would be terrifying. Thankfully, though, I don't think we'd have to worry about that too long thanks to pewter's rapid burn rate.