Since the Dark Mimics only make you draw cards and don't make you do other things:
- Dark Mimic LV1: You only draw a card, you don't send the card to the graveyard along with that.
- Dark Mimic LV3: Only makes you draw cards when its effect is activated.
You should be able to chain with Null and Void. I'm just not very sure if it could be possible to use Null and Void against Dark Mimic LV1 in the Flip Monster section of the Damage Step, knowing that it is possible to use Null and Void against Airknight Parshath in the Damage Calculation section of the Damage Step. Hmmmmm.... It should be possible...