This is an interesting question. Much of Greek and Roman ideas were preserved through Islam through Christianity. When Islam took over more land, often times they had Christian scholars teach them about ancient learning. The Christians were the heirs to the Greco-Roman world. Philip Jenkins, a professor from Penn. State has written extensively on this topic.
From this perspective, the answer is more complex. Yes Islam preserved, but they did so through Christian scholars.
As other editors point out, Islam "inherited" many of the lands and ideas of the Greco-Roman civilisation, and their preservation and incorporation of them into their culture ensured the survival of so many discoveries and pieces of knowledge. This enabled the whole world to benefit from them over the course of history.
An important element of the Islamic preservation of Greco-Roman culture is that Islam preserved the works of Aristotle when they had long been lost to the West. When Christian knights invaded Toledo Spain, Aristotle was re-discovered to them. Because Aristotle argued that one element could be transformed into another, he appeared to confirm the Church's position on transubstantiation, that is the belief that during the Eucharist the bread and wine were transformed into the body and blood of Christ. Since he therefore apparently "agreed" with the Bible, Aristotle and the Bible became the only accepted authorities; an intellectual discipline known as Scholasticism. Interesting and ironic that this discipline would never have taken root without the preservation of the Muslims.
Google Books is a good place to look for information about questions such as the ones you've raised. Google Books offers extensive previews of many books. (So does Amazon; you can use their preview feature if you have an Amazon account, which costs nothing.) The best books to look for are ones that have been peer reviewed -- in other words, assessed and approved by other experts. Usually these books are published by university presses. Anyone can publish a book these days (just as anyone can slap up a web site or post to wikipedia), so it's even more important now than it was in the past to look for information that has been peer reviewed. Here is a good place to begin a search of the topic you've raised: http://www.google.com/search?q=karl+marx&btnG=Search+Books&tbm=bks&tbo=1#sclient=psy-ab&hl=en&tbo=1&biw=1366&bih=600&tbm=bks&source=hp&q=islam+and+the+greeks+and+romans&pbx=1&oq=islam+and+the+greeks+and+romans&aq=f&aqi=&aql=1&gs_sm=e&gs_upl=246246l254078l0l254593l36l26l0l2l2l0l329l4970l0.11.11.2l28l0&bav=on.2,or.r_gc.r_pw.,cf.osb&fp=fdea6ba8f51ecf36
An important fact to consider is that much of Greco-Roman culture that passed through Islamic translators became altered to fit into Islamic beliefs. Originally, many works were translated not for their knowledge but as vanity pieces to be displayed but not studied. It was only later that the Abassid Caliphate took steps to learn from Greco-Roman books and art. In both situations, however, translators fit much of their translations to accepted Islamic belief structure, so as not to be accused of distributing heretical material.
The influence is that many Greco-Roman beliefs were transmitted through Islam. Most of the rest of the world had forgotten about the Greeks and Romans, and the Islamic philosophers dug up old Greek and Roman manuscripts, translated them, and incorporated them.
I have found a link you might like. It also includes links to other references.
The ancient Greek and Roman Empires had both long since ceased to exist when the Islamic religion arose and began to spread throughout Asia in the 600s CE. As a function of geographic location, the area that gave rise to Islam had historically been more influenced by the Greeks as a result of trade and travel along the eastern Mediterranean Sea islands and coastline.