It sounds like, in this case, the OP is talking about the EEPROM holding code executed by the embedded coprocessor on the NIC (or, at least, lookup tables that the coprocessor uses) rather than a PCI option ROM that will be executed by the host computer's CPU. Depending on how the access to the EEPROM is performed (i.e. if such access is facilitated by the co-processor versus being read out directly from the EEPROM) I'd think an attacker could even implement "stealth" functionality to allow the compromised EEPROM to appear to be benign when audited.

Depending on what functionality is being offloaded to the NIC (are there still NICs that do IPSEC and crypto offload?) there's the possibility for information disclosure vulnerabilities in the NIC itself. Yikes.