Does Astral Heron also cover additional costs such as accelerate?

Yes. Astral Heron's discount applies to the total cost of your next card, and discounts can reduce additional costs like Accelerate — even down to 0 (Rule 356.4.f).

So if your discounted card has Accelerate, the [2][A][A] covers the Accelerate cost too ([1] Energy + [1] domain Power), since the [A][A] portion can pay Power of any domain. You still need to actually choose to pay Accelerate for the unit to enter ready — a 0-cost additional cost is still "paid" if you declared it (Rule 356.4.f.1).