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I wonder if the Caesar 3 download offered by GOG contains the patch that enables you to turn off the god effects? Can anybody please let me know?
I don't know.

But I highly recommend anyone wanting to play Caesar 3 just grab the open-source reimplementation of it:

This one aims to be vanilla compatible with just a little bit of UI polish and modern system compatibility, and that makes all the difference. It runs properly in a window and at any resolution, it runs smooth at high speeds, it can (optionally) display some info like unemployment rate in the side panel, if you don't want to click through advisors every time.. it can (optionally) display the range of fountains, wells, and reservoirs when you're building them. It fixes a few visual glitches, such as aqueducts leaving an intersection (until you rotate camera) after the intersecting part of it is deleted. You can set warehouses to "not accept" everything with one click instead of clicking each item separately. It does have a few toggles for turning on just a couple bugfixes that affect gameplay (you don't have to turn them on though).

And it does indeed have the option to turn off god effects.

Absolutely superior to vanilla in every way, with no forced gameplay changes that would make it into something different. Heck, it should even be compatible with vanilla saves.

For those who want additional gameplay changes (e.g. road blocks), there is a fork of Julius called Augustus: