Can Heedless Resurrection play the unit sacrificed for it as cost.

No. You cannot resurrect the same unit you kill to pay Heedless Resurrection's cost.

When you play Heedless Resurrection, targets are chosen in Step 2 of playing the card — you must pick a unit already in your trash. The unit you're about to kill is still on the board at that point, so it's not a valid target. You pay the additional cost (kill a friendly unit) in Step 4, but by then the target choice is locked in and can't be changed (Rules 355.9.a, 355.15). You'd need a different unit already waiting in your trash.