It depends on how entangled God is with the rest of us. If He can make the observation, and then keep a completely straight face forever (never leak any information about the result in any way), then His mighty observation would not collapse the wave, from our perspective.
That’s why sparrows can be in so many places! (Matthew 10:29)
When you hear about “observations”, in the context of quantum mechanics, it usually takes the form of some smart-looking, glasses-wearing, dude saying things like “a particle is in a ‘super-position’ of states until someone observes it, and then suddenly it’s in only one state”. The misconception here is that the universe as a whole (which includes people and Gods and whatnot) is in one state, and only tiny things can be in many states.
The traditional thought experiment for talking about this is “Schrödinger’s Cat”. Schrödinger puts his cat into a purfectly information-proof box, so that there’s no way to see what’s going on inside. Also, he rigs up something deadly that has some chance of killing the cat in the next day or so. Before the box is opened, the cat is both alive and dead, but afterward the cat is either alive or dead. The cat undergoes “wave function collapse”.
This is a metaphor for, for example, the photons in the double slit experiment. Each can demonstrably go through both slits, but if you determine which slit a photon goes through, then it only goes through one.
Unfortunately, this has been taken as a rallying cry for a lot of bad physics. A better thought experiment (and one which gets closer to explaining the answer to the question) is “Schrödinger’s Graduate Student”.
Repeat the cat in a box experiment, but this time Schrödinger finds that, overcome by quantum grief, he cannot bring himself to open the box. Instead, he goes out for tea or something and has a graduate student complete the experiment for him. Once done, the student then finds Schrödinger and reports the results.
But, since Prof. Schrödinger hasn’t observed the graduate student yet, from his perspective the cat and student are still in a super-position of states. The only difference is that now they’re entangled. They’re in a combination of the “dead-cat/horrified-student” and “living-cat/cautiously-optimistic-student” states. When the student finally reports the results to Schrödinger, then the cat/student wave function collapses (from his perspective).
In practice of course, there’s information leaking all over the place. Considering all of the different paths that information can take: chemicals, air movement, stray photons, gravity, etc. it’s really hard to construct “information-proof-anythings”. If someone on the far side of the planet sneezes you’ll be entangled with that event within moments. That’s not saying as much as it sounds like it is. Essentially, you don’t have to worry much about “big and nearby” events (like sneezing on Earth) being in multiple states.
So, say there’s a God, and say that he/she/it/they/we observes every quantum event. As far as each of us are concerned, unless God somehow conveys the information (burning bush, cheeky glance) he’ll/she’ll/it’ll/they’ll/we’ll be in the same position as the graduate student was before he delivered the results to Schrödinger.
So, in order to keep a quantum event many-stated and quantumy (from our perspective), all that an all-seeing God needs to do is play it cool, and not reveal any clues, whatsoever, about that event.