What happens if I play Atakhan from my deck with Rek’Sai, Breacher on the board? Can I pay the Accelerate cost and kill Rek’Sai for the Atakhan additional cost? Will it enter ready?

Yes, as long as you pay the Accelerate cost, Atakhan will enter ready, even if he kills Rek’Sai for his additional cost. This is because Accelerate creates a delayed replacement effect that causes Atakhan to enter ready. Although he lacks the Accelerate keyword when he resolves, he still has the delayed replacement effect that Accelerate generates.