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Can the NT4H originality be validate without configuring a random ID (nt4h_rid_read_ecc_signature_pk ECC signature)?

Is it possible to validate originality on the NT4H (using ECC signature from nt4h_rid_read_ecc_signature_pk) without configuring the Random ID as described in your API docs, as I can do this using the NXP SDK without a Random ID configured?

Yes. In case the Random ID is not configured, you should use the following function:
UFR_STATUS ReadECCSignatureExt(OUT uint8_t *lpucECCSignature,
                                                               VAR uint8_t *lpucECCSignatureLen,
                                                               OUT uint8_t *lpucUid,
                                                               VAR uint8_t *lpucUidLen,
                                                               VAR uint8_t *lpucDlogicCardType);

You can examine the code with
Function void check_signature(void)

If the UID length is 4, then Random ID is activated and you should use function nt4h_rid_read_ecc_signature, if UID length is 7, then this is a regular UID and you should use function ReadECCSignatureExt.