I love the SIMS!! All the way back to PC based SimCity.
I am familiar with The God Mode. If I'm not mistaken, the Sims also used to have a Free Will option you could set to have the Sims carry out daily activities and not require you to make them do each task. Interestingly enough, the (the algorithm) was based on the personality traits assigned to the individual Sims.
To answer the question - I suspect that whoever is controlling or has the power to control might be perceived as a God, but that doesn't makes them a God.
I suppose we would have to define "God" before the question, certainly in this specific case, could be answered.

It seriously depends on what the definition of god is.

If you can do anything and everything in god mode, then you all you have to do is make them not think like that or reprogram it.

As a programmer, I can assure you that there is very little that is god-like about coming back to your desk after three hours sleep on the fourth day of a programming "death-march" to code for another 18 hour session and being unable to find your mouse or keyboard because of a giant pile of Mountain Dew cans, candy wrappers, take out boxes, printouts, and a whole bunch of those little phone message slips with your bosses name and number and the words "Call me ASAP!!!" written on them.

Gods, as a rule, are generally credited with the ability to create worlds. In this scenario, it would aptly apply. Just as it is easy to imagine that we're no more than a simulation, witj what we perceive to be a very high resolution concerning graphics. How would we know without direct contact with our creator? Another reason religion still exists, I'd wager.

Simple enough. The big difference os that programmers are limited both by the physical machine’s limits, and the limitations of logic (i.e. can’t make a program that isn’t internally logical). People claim god is all powerful, that he has no limits of any kind.

A machine that has become self aware would be correct to call us gods only in the sense that we designed and created them. How you would disuade them would largely depend on how they were programmed to learn, as machines do not interpret the world the same way we do.

Your hypothetical has too many unknowns for me to venture a guess. It is possible to characterize at least one special case. If God is omnipotent, then it can break the laws of physics. If God built 1000 O'Neill Cylinders overnight and moved half the Earth's population into them, then I'd believe in God. That God might be the simulation programmer of whom you speak. There's no way to know.

If they were intelligently designed they wouldn't believe in gods.