Interesting questions, so I went through a few books.
The metal fan guard, on the top of the radiator, was standard on all GTO's unless.... you had a fan shroud.
The fan shroud was used on 1966-'67 GTO's with A/C, Part No. 9783757 and the inside diameter measured 21 1/2" matched with a 19 1/2" diameter, 7-bladed, clutch fan.
The same shroud was used on the 1967 RA engine, but with a 4-bladed metal fan. However, not all RA engines had the shroud.
Another fan shroud was also offered from 1964-'67, Part No. 9774621, with an inside diameter of 19 1/2" and was used for the optional trailering package or for field installations of A/C. It could also be used/added on any 1964-'67 non-A/C GTO having the 18" 7-bladed clutch fan. Looking at the AMA specifications, all non-A/C GTO's used the 7-bladed 18" clutch fan as standard equipment.
That said, it would appear that factory installed fan shrouds fall under 4 categories for the GTO - (1) only those cars with A/C were factory fitted with a fan shroud. (2) Some, not all, RA GTO's were equipped with a factory fan shroud. The (3) optional trailering package included the factory fan shroud, as did the (4) field installation (dealer) of an A/C set-up (just as a factory ordered car would have been equipped).
A fan shroud could have also been an add-on to any GTO with the standard 18" clutch fan set-up - perhaps by a dealer or over the counter. I suspect some racer types, those in hot regions of the country, or even those who did not order a trailer package, but pulled a trailer of some kind.
If the GTO in question has the metal fan guard on top of the radiator AND
a fan shroud, then it is almost certain that the fan shroud was an add-on and not factory.