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Using Occam’s Razor to cut to the chase:

Don’t you think if the Pantheon had been designed to be used as a sundial that at least one Roman writer from antiquity would have mentioned it?

“I was walking through the Forum and popped in to the Pantheon to see if I was late for dinner.”

I agree it is unlikely the Pantheon was used to tell time. Still, if it was being rebuilt with a hole in the top of the dome most architects would probably think this would be a cool feature to incorporate in the design. Maybe the priests asked for it?

I love that building; it's so well preserved. It's like a time machine back to ancient Rome.

I think they had in mind a finished dome, but (as the dome is concrete), bridging that nearly-flat last bit may have looked like they were pushing the envelope a wee tad. And of course, the interior would have to be illuminated by some means. And excess rain is rarely a problem in Rome. Also, finer Roman houses included both the atria (the still oft-copied roof with a view) and in larger houses the peristyle, both of which are at least partially open to the sky.

http://www.monolithic.com/stories/the-pantheon-rome-126-ad

[snip] Just about everything had to come down the Tiber by boat, including the 16 gray granite columns Hadrian ordered for the Pantheonâ€™s pronaos. Each was 39 feet (11.8 m) tall, five feet (1.5 m) in diameter, and 60 tons in weight. Hadrian had these columns quarried at Mons Claudianus in Egyptâ€™s eastern mountains, dragged on wooden sledges to the Nile, floated by barge to Alexandria, and put on vessels for a trip across the Mediterranean to the Roman port of Ostia. From there the columns were barged up the Tiber... Eventually, work began on the concrete dome, constructed in tapering courses or steps that are thickest at the base (20 feet) and thinnest at the oculus (7.5 feet). The Romans used the heaviest aggregate, mostly basalt, at the bottom and lighter materials, such as pumice, at the top. They embedded empty clay jugs into the dome’s upper courses to further lighten the structure and facilitate the concreteâ€™s curing. [/snip]

for the scale:

http://www.monolithic.com/stories/the-pantheon-rome-126-ad/photos/2
http://www.monolithic.com/stories/the-pantheon-rome-126-ad/photos/3
http://www.monolithic.com/stories/the-pantheon-rome-126-ad/photos/7
http://www.monolithic.com/stories/the-pantheon-rome-126-ad/photos/8

It became a church in 609, was looted by Emperor Constans in 663 (wiki-wacky-pedia).

In before the “this is just speculation” and “who cares this is just a scam for grant money” morons arrive.