Hi,raja, I have the same intuition with you from Allen's book. For your question, I think that op amps is designed in the way that the first stage gives the dominant pole and the second stage give the non-dominant one, just as the first stage is always the transconductance stage and the second be buffer with high output current.
If what you assumed happen, we should use other ways to compensate the opamp and perhaps Miller compensation will fail.
Hope helpful.
Best regards.
jqjqjq

Raja,

You should derive the exact transfer fuction using Gm and Ro models for first and second stage to get the complete picture which can confirm the intuitive results. Here's a couple of things which will happen in this case:

1. Given: second stage output pole is dominant.
2. Application of miller is valid only upto the second stage pole frequency as after this frequency the second stage gain starts falling with 20 dB/decade. You might still be able to use miller gain but then you should use A2(s), and not the DC value of A2.

3. Intuitively, I can say that the second stage pole will decrease by a smaller amount as long as A2 at first stage pole frequency is greater than 0 dB. Second stage pole frequency will decrease because Cc is not acting as a short between gate and drain of second stage MOSFET if it is smaller than the ouput capacitance of second stage. Hence, both second stage pole and first stage pole will decrease while first stage pole will decrease rapidly.

4. When compensation cap is made larger than the output capacitance of second stage it will act as a short between gate and drain of second stage mosfet and the second stage pole will increase as Cc is increased.

5. At around this frequency or when compensation cap is made very large (compare to output cap of second stage) first stage pole becomes dominant and the usual pole splitting behaviour should be observed thereafter.  

All these observations are intuitive and only a complete analysis could establish their reliability.