If Card car D and Rescue Rabbit (and some alike) is Effect Veilered or Fiendish Chained:
1.) Card car D/Rescue Rabbit gets effect veilered, he can tribute itself but WONT be able to draw 2 cards.
2.) Card car D/Rescue Rabbit gets fiendish chained, he can tribute itself and WILL be able to draw 2 cards.
Also worth noting, is they'll have to be Veilered or Fiendish Chain on Summon, because if you chain it on activation, Veiler and Chain will have no target, since they banish/tribute as cost, which immediately happens
*Costs can't be negated which is another thing.