ITN: Does a Partner Organisation need to indicate the PIC in the A forms?

No, this is not needed, but encouraged.
GfA p. 31:

Partner Organisations
Information on partner organisations is provided by the coordinator ONLY under section A5 of the proposal. Although not mandatory, providing a Participant Identification Code (PIC) for partner organisations in section A5 is encouraged.

Notice that there has been a correction regarding the Part A application.  It is under Additional documents on the  Participant Portal:

Erratum for the GfA - 22.12.2015
Applicants to the call H2020-MSCA-ITN-2016 are advised to take note of the following erratum in the Guide for Applicants.
Partner Organisations in Section A of the Proposal
On page 31 of the Guide, it is stated that information on partner organisations should be provided under section A5 of the proposal. Please note that this incorrect. As should be clear from the submission system, information on partner organisations should instead be provided under section A1.

You have to register the Partner Organisations in three places: 
1) Part A Section 1
2) Part B in the list of participants in the beginning
3) Section 5, second word/pdf document, where there is one type of table for beneficiaries and another one for Partner Organisations.