Final answer:
Diphtheria does produce an exotoxin that inhibits protein synthesis in eukaryotic cells by inactivating elongation factor 2 (EF-2), which is essential for protein synthesis, therefore the statement is true.
Step-by-step explanation:
The statement that diphtheria produces an exotoxin that inhibits protein synthesis in eukaryotic cells is True. Diphtheria is caused by the bacterium Corynebacterium diphtheriae, which secretes an A-B toxin. Once inside the eukaryotic host cell, its A subunit transfers an ADP-ribose molecule to elongation factor 2 (EF-2), a key protein involved in the synthesis of new proteins. This action inactivates EF-2, thereby halting protein synthesis and leading to the death of the host cell. This mechanism plays a crucial role in the disease pathology of diphtheria.