--- In firstname.lastname@example.org
> Just wondering if I can mix the heads and tails along with the
> it through the carbon filter for vodka.
No. The purpose of distilling is to remove the heads/tails and
excess water and heavy flavinoids from the spirit (body). Why would
you want to add them back?
Carbon is a mechanical filter. It works well on substances with
relatively large molecules i.e. larger than ethanol. It doesn't
work at all on the lower BP substances like methanol and ethyl
acetate (the 'heads').
If you want to make vodka, take the body at > (greater than) 95%abv,
then water it down to drinking strength with bottled water. Avian
water from France works well.