Since the Employer is not & cannot be a third party under the Contracts (Rights of Third Parties) Act 1996 under the NEC3/4 provisions, does that imply that the Employer has an automatic/implied right to enforce a term of the main Contractor’s subcontracts by virtue of being identified in the Contract Data Part 1? Or is the right to be expressly conferred via a collateral warranty??
Generally speaking ‘privity of contract’ means that only a party to a contract can take benefit, or be subject to obligations, under a contract. Furthermore any action in Tort is also unlikely to succeed as it would be extremely difficult to establish a ‘duty of care’ (see D&F Estates Ltd v Church Commissioners for England and Wales  AC 177;  2 All ER 992).
The Contracts (Rights of Third Parties) Act 1999 changed the position of ‘privity of contract’, however, whereby a third party, including the Employer / Client, could have rights under a contract between a Contractor and Subcontractor as a third party, but only where they comply with the requirements of s1 of the Act. This would mean being expressly identified by name (member, class or description) in the contract. For clarity it would also be beneficial to state what clauses this right(s) applies to and how they are to be applied. If this is the intention then NEC Option Y(UK)3 would be appropriate in this instance, with the Employer / Client named as a ‘beneficiary’.
Alternatively a collateral warranty may be used which would essentially infer the same rights as those under Y(UK)3, although this would have to be signed by all parties and executed as a deed for ‘consideration’.
Being named in the Subcontract Data does not automatically mean that the Employer / Client is entitled to enforce any third party rights, unless specifically identified as such. The Project Manager and Supervisor are also included, but you would not expect either of them to gain such rights just by being named.
I would suggest using either Y(UK)3 or a collateral warranty. Both achieve the same end result but by different means.