Intel does not use third-party driver for NVMe, so we cannot confirm whether it is going to work or not. We advise to use our official driver from our download center found in this link: Intel® Download Center
Are you having a problem getting you're P3700 to boot with this new system or is this a more of a 'theoretical' question?
If you are having a problem, please provide motherboard model, BIOS version and the firmware version installed on your P3700.
Also, does your system show the version of the BIOS NVMe driver?
Currently I have no problems on booting yet, but the device name of the P3700 has changed in the BIOS screen (American Megatrends's driver does not display the SSD serial number as part of the device name but Intel's driver does).
My system BIOS does not show me the version of the NVMe driver.
I have even dumped AMI's NVMe driver from the UEFI shell via "dmem", however looking at the content of the entire file it does not show any kind of version.
I am also currently pursuing this with ASUS support to give me the option to choose which UEFI driver to load (or turn AMI's driver on/off).