If I use Heedless as the attacker, can I play a unit to the battlefield I was attacking?

As the attacker, no, you cannot play the resurrected unit to the battlefield you are attacking.

According to RiftJudge FAQ #9753 and the related ruling logic:

• Battlefield Control: During a showdown, you do not control the contested battlefield. Because you are the attacker, your control is restricted to your own base (and potentially other battlefields you occupy), but you cannot play units into the battlefield you are currently attacking.
• Heedless Resurrection's Restrictions: While Heedless Resurrection creates a chain that allows you to play a unit from your trash, that unit must be played to a valid location. As the attacker, the contested battlefield is not a valid destination for you to play a unit.

Summary of the interaction:

1. You initiate the Heedless Resurrection chain as a [Reaction].
2. You pay the cost (killing a friendly unit).
3. Even though Heedless Resurrection is on the chain (keeping the game state closed), you still cannot play the resurrected unit into the battlefield you are attacking, because as the attacker, you lack the required control of that battlefield to place a unit there.