Sorry if this has been asked elsewhere, but I want to know if the P9 has a setting that exactly replicates the A9 protocol?
Yes, the P9 uses identical firmware to the M1, which includes current and legacy A9 pulse protocols. The P9 also has several hardware improvements, is powered by a 9V battery, and has the option to use internal coils.
The pulse protocols of the P9 (and M1) are listed on the quick start card:
On the second page of the PDF, the pulse protocols are listed. The second protocol is the A9 legacy (older) protocol, listed as - -A9- -.
The fourth protocol on the list is the Omni8 protocol, listed as - - Omni8 - -, which has been the protocol used in newer A9 systems, since May 2016.