So, let's assume that some lucky scientist actually finds a scientific rather than faith-based proof of the existence of God. Hey, let's go one better and assume that Anne and I are the lucky scientists (we want the Nobel prize money and the appearances on Colbert)! For the moment, let's just say we proved that God is something person-like (whether or not He/She/It has various unmentionable organs, hands to be on the right side of, form to be the image and likeness of, or eyes for us to be pleasing to the sight of.
Now, what would the impact of that be for science?
Of course, the immediate impact would be great relief that we will, after all, have an after life, assuming we don't use our science for greedy or harmful purposes (well, that may exclude a lot of us from the pearly gates).
First, the God we prove might act in a deist way: He/She/It created the Universe, gave it some laws to run by, and let it the go off on its own without further intervention. This, after all, is a concession that some scientists, even Darwin, have made to religion as a possibility. In that case, the nature of science would not change one iota. We would just, for self-praise, newsiness, and grantsmanship, change our rhetoric to say that we propose this or that study to understand God's laws--think of the 'significance' section of our grants!! But novel? Not a bit of it! That was what the greats like Newton were explicitly doing centuries ago.
Alternatively, we might say that God did create things-as-they-are, and that our job is to characterize the mind of God in that way, but that occasionally God intervenes in mundane affairs. He/She/It might do so in answer to a prayer, though it's hard to see how so puny a thing as a single human could have such influence on the Eternal Omniscient, and specific tests of the efficacy of prayer have bombed completely.
Nonetheless, what that means is that when an experiment to characterize the laws of Nature--the same experiments we do anyhow--didn't work, our explanations would have to include the possibility (besides that our theory was wrong) that God altered the pH of our reactions. But in practice, that would just another source of occasional measurement or experimental error in our analysis and interpretation.
Ad hoc interventions by the deity would be singleton events and science usually is not designed to identify cause in those cases, in the same way that one-off lab errors or sample design flaws often can't be identified. That's why we repeat experiments. We already accept that odd occurrences do happen, and our inference about theoretical validity is, and would remain, statistical in the face of occasional divine speed-bumps. Because intervening in that way by definition means that there are laws of Nature to intervene with. So nothing in routine science would change on that account.
Even if God always intervened in the same way if we repeated the same experiment (the wily imp!), that would be just another kind of special case of, or change in, the law of Nature that we're trying to understand.
In any case, the evidence is already prohibitively strong that the universe is law-like, so that such interventions cannot be too common. That's why literal religion has such difficulty with scientists in the first place! Indeed, some physicists speculate that the laws of Nature are no such thing, they are just generalizations about our particular place in the universe, or our particular universe in the universe of universes (i.e., that we could get to if we could sail through black holes).
And what if the proof sees 'God' only, as we've been already warned, through a glass darkly? What if God is not person-like and can't be interpreted as such, or doesn't respond to human events that way? What if He/She/It is something more abstract, like the Oneness of Buddhism, or the varied origin stories of different cultures around the world. Or what if He/She/It is more remote and distanced from us rather than a conductor bothering to steer our puny earth on its daily mundane way? How could even science that proved that He/She/It existed use that knowledge to interpret things any differently than we already do? Again, the world clearly appears law-like, and science is a set of methods to understand those generalities of how-things-are. If science has imperfections in understanding Nature, maybe it's our reliance on current methods and concepts, that we inherited, after all, from the Enlightenment period a few centuries ago and need not be written in stone.
If some clever person suggests a different way to study what we call transcendental or immaterial realities themselves, and showed that your brain really can communicate with He/She/It (or your long-deceased ancestor or pet dog), that would open up a whole new (and extremely exciting) realm for human research. But it wouldn't change how-things-are in the material world that we already know about.
Overall, knowing that God exists might make a big difference to scientists personally, but would not make any major difference to science, except returning its rhetoric to something that goes back to classical times. Just as accepting evolution doesn't make a major difference to creationists, or even many scientists, in their daily work.
These things are at least worth thinking about--they help clarify the true nature of the science-religion debate as a conflict over cultural resources, rather than one about the physical realities of the world.