Before we even begin to answer the question "could God have used Evolution?" we need to first understand that there are two possible interpretations. The first is whether or not it's possible that He actually did. The second is, regardless of whether He did or not, is it within His abilities?
In Titus 1:2 (among other verses) we are told that God cannot lie. This is actually a very good thing. If God could lie, a Christian would be no better off than a Muslim. We could have one foot in Heaven and still fear God's deception (Khalid Muhammad Khalid, Successors of the Messenger). You simply cannot afford to have an omniscient, omnipotent deceiver in your worldview. If you can't trust the source of truth, you can't trust anything. Not their message of salvation, or their message of origins. Everything you believe could be a lie.
But as I said, we have the exact opposite. We have a God who literally cannot lie. Therefore, we can trust His message of salvation. But what about His message of creation? The answer to that is an absolute yes. In 2 Timothy 3:15-17, we are told that all scripture is "God breathed". And again relating to salvation, Jesus said that if we believe Moses (who wrote Genesis - Deuteronomy), we would believe Him (John 5:46). So, here we have a God who cannot lie inspiring all scriptures, including Genesis, with a special emphasis on Moses. What that means is that the Creation account in Genesis is absolute. If you don't believe it, you either believe God lied, or that God made an error. Alternatively, you are claiming God didn't inspire scripture, but at that point, you have no authoritative source of doctrine and are left fumbling in the dark with the unsaved.
Thus, the answer to the first interpretation of the question is no, God absolutely could not have used Evolution. He cannot lie, and He has told us that He created the heavens, the earth and all within them in 6 days, that man was a special creation created on day 6, that death didn't even enter the world until Adam sinned, that there was a global flood, that the entire human race was dispersed from Babel, and that all of this happened within the last 6,000 years. Evolution is simply incompatible with the Biblical view of origins, therefore God could not have used Evolution.
But what of the second interpretation? Is it possible that God could have used Evolution if He'd wanted to? I strongly contend that the answer is actually no. To explain why, let us first go back to Titus 1:2. Here, you'll find an interesting concept. We're not just told that God doesn't lie, but that He actually cannot lie.
This is where things get confusing. The average person thinks that God should be able to do literally anything, even the impossible. He should be able to make a round triangle, or make a rock too heavy for Him to lift (and still lift it), or make 2 + 2 = 57 a true equation. But this isn't Biblical omnipotence. There is one limit on God's abilities: His own character. God cannot lie because God is too perfect to lie. There are things God cannot do simply because they are not Godly things to do.
You can actually understand this from a little self examination. There are many things which, while they are well within your physical capabilities, you "cannot" do. You can stab yourself in the eye with a ballpoint pen, but why would you want to? This is so repugnant to your own nature that even though you can do it, you also can't do it. We even know that God is capable of lying, because His word records, word for word, the lies of other beings. God can quote any lie Satan tells. But to actually tell those lies Himself is as repugnant to His nature as self-mutilation is to yours, to the extent that He just couldn't do it.
So the question we must ask is whether or not Evolution would be within God's abilities, but rather, is it within His nature? In Deuteronomy 32:4, we see why it certainly isn't. Here, we are told that all God's works are perfect, and all His ways are just. Can this be said of Evolution?
First, let us consider God's reaction to each of His creative acts in Genesis. After most of the days (day 3 being the exception), He sees what He has made, and declares "it was good". Only after Adam and Eve, the first man and woman, are created, does He finally declare "behold, it was very good".
Now let me ask you a question: Is cancer very good? I hope none of you would say yes. You don't even have to personally experience cancer to know it's not a nice thing. It is a slow, painful destruction of something else that is very good. Yet we see cancer in the fossil record. It even affected dinosaurs. Is this good? Is this just? Why should dinosaurs suffer with cancer millions of years before sin even entered the world? Why would God look down on a world filled with cancer and call it "very good"? And cancer is just one cause of death. Death itself, which the Bible calls an enemy (1 Corinthians 15:26), is the very mechanism by which Evolution supposedly happens. So, we're not only supposed to believe God used billions of years of death and suffering just to create us, but He was having a bit of a laugh about it while He did so? Is that your God? It's not my God.
Evolution carries even more implications. Let us see what Charles Darwin thought about other races: "At some future period, not very distant as measured by centuries, the civilized races of man will almost certainly exterminate, and replace, the savage races throughout the world." In Evolution, there is a progression from animal to man. Some humans, if Evolution was true, would be more closely related to our ape like ancestors (and to other apes) than others. Darwin even claimed that the distance between whites and the so-called "savage races" (i.e. anyone who wasn't white) was greater than between a wild and domesticated animal. Now tell me, my brethren, does this sound like a God who is without prejudice? A God so vindictive that if you're not a white man, there's a greater distance between you and white men than between a wild and domestic pig, is a perfect God? Because the God I believe in doesn't care about the melanin content of your skin. Whether you're red, yellow, black, or white, He loves you equally.
Just as Darwin and the early Evolutionists believed non-whites were inferior to white people, they also believed that women are inferior to men. Whereas the Bible describes complementary roles for men and women, men are not seen as intellectually or spiritually superior. In Evolution, by contrast, there is the theory of sexual selection, wherein women have evolved to be inferior because men prefer inferior wives. Indeed, the whole "smaller brain, smaller intellect" thing came from Darwin's assumption that women generally have smaller brains than men, and thus men are generally intellectually superior. Yet, in the Bible, wisdom itself is personified as a woman! That's how much God values women.
So we see, just from these three examples, that Evolution is so contrary to God's nature that it simply wouldn't be possible for God to use it. It's disgusting, it's unjust, it involves nothing but brutality and prejudice. I thank God every day that He is not the God of the Theistic Evolutionists, because if He was, the difference between Heaven and Hell would be equal to the difference between the first and third world countries we already have here on Earth. Therefore, I firmly believe we can say "no, there is no sense in which God could have used Evolution to create."