No, pESN is not for network ID purposes, it's a legacy ID just for back end network services that doesn't support MEID system yet, like texting, and it's calculated using the MEID. What you have to do is ask if your network supports MEID in their system and enter the MEID instead of the pESN.
If you want to learn some more check this very good explanation on MEID/ESN/pESN--->
http://www.howardforums.com/showthread.php?t=1360767