Only if by "if you rush" you mean eat in about 15-20 min will it get you near the front of any entrance. There will be people lining up at those ropes by 8:15 and by 8:45 (which would be my definition of rush), there will be quite a crowd at each of them.
OP if you want to eat at CP, make an ADR for around 10:30 and enjoy the early morning touring attractions.