If we are talking about the Christian God, then yes. But if we are talking about a God in general, then no. I am going to assume that the question is only referring to the Christian God.
The only evidence of the Christian God's existence is the bible. This holy book, called the bible, makes claims to the contrary of Evolution. Evolution has years of research and science behind it, and it has been subjected to much scientific critique. It is extremely unlikely that Evolution is incorrect so for the bible to be at odds with it, forces honest people to question its accuracy. But the bible isn't only at odds with Evolution, it is at odds with other areas of science; considering, the magical stories told in it.
So if we are talking about the Christian God, who's existence is based on this book, we have to conclude that Evolution is the evidence of the absence of this God. Since the two ideas, the Christian God and Evolution, are not compatible, we have to recognize that one has to be wrong. Either the bible, and the idea of this Christian God does not exist, or evolution does not exist. And there is the small possibility that both are wrong. But two contradictory claims cannot both be right.
Genesis is the foundation that the bible stands, without it, the rest falls. Genesis contains the largest examples of gods power in both crating and destruction. Without such claims of power, the Judeo-Christian god has little to claim of it's power. It could also raise the idea that if their god did not cause creation, some other more powerful god must have.
Genesis is also key to Christianity. According to the bible, mankind inherited sin from Adam and Eve. It then states that Jesus die in order to pay for our inherited sin. If Genesis is false, then the death of Jesus had no purpose and the motive too is just a lie. The New Testaments make many references to events in Genesis. Clear if Jesus was the son of god or god in human form (depending on the belief) then he would know that the event in Genesis never happened. This would mean that Jesus not only gave himself to what he knew was a lie but that he preached the lie to his followers.
A lot goes toward credibility. If a book about U.S. history claimed that the North American continent was man made, as if someone like Columbus literally build the continent, would you be willing to believe that the rest of the history book is accurate?
Clearly, without Genesis as fact, the rest is just as fictional.
I like Sooner's comparison. To explain further on his point, religion tells us that God invented creationism making it a law of the program, however if evolution is true, it only disproves creationism which is separate from everything else. All it does is change one aspect of the playing field.
Or the way I like to put it: If I tell you
2+2 = 4 and
Blue and yellow make orange
Then the false statement I made about blue and yellow making orange has absolutely nothing to do with the truth of two plus two equaling four.
If I were creating a simulated game, I might make a program by design, that randomly does what the "Theory of Evolution" is proposed to do. It would be the perfect system to get random people instead of arranged robots. It just depends on how the god wants to do it and what their motive/want is.
If you're a believer, you'd know that Adam and Eve were the first people. Scientists don't have actual proof that we evolved. Just because you go to a museum to see ancient human bones doesn't mean that they were the earliest humans. The first people were Adam and Eve. Like it says in the bible, Jesus uses his holy power to heal and stuff. He doesn't do it anymore so he can test us modern people to see if we believe and if we have the faith.
Evolution would only disprove God, or specifically the Christian God, if we insist on a literal interpretation of the first chapter of Genesis. There have been Christians going back at least as far as the third century AD insisting that the first chapter of Genesis should not be taken literally. The style in which it was written and the way it was positioned in the in the book suggest that it was not intended to be read as a literal account.
Many Christians and other theists might have a less literal interpretation of Genesis. Most people whom believe in god around the world do in fact accept Evolution. There's no saying God couldn't have controlled Evolution, or that God gave life the ability to evolve from environmental changes, and etc. God controlling Evolution is a possibility, even though I myself am a little skeptical of a deity existing.
I am referring to the Christian God. Charles Darwin, the biggest contributor to the evolution theory was a Christian when he wrote "The Origins of Species". Evolution was never meant to disprove God. It was merely showing the complex processes it place.
In labs, scientists were able to make E. Coli evolve. Most atheists would claim that this proves that we evolved from a single cell organism but this is impossible. The E. Coli merely changed species, but it was still E. Coli. It is impossible for it to change into a complex organism over the course of billions of years. In my opinion, this is one of the biggest misconceptions. A bird can evolve into a different species, but it cannot, ever evolve into a totally different kind. We have no proof.
We can never be sure how evolution occurred. Secular theories are continue been rewritten over and over again. The Bible only has to be written once. No updates whatsoever (Besides translations). After 3000+ years, our knowledge is still not enough to disprove the Bible.
Evolution can clearly be used to support God, but it is clearly harder the other way.