What if Tamerlane the Great had never lived?

Tamerlane the Great, Timur the Lame, had precisely the kind of life and career that Adolf Hitler really wanted for himself. Tamerlane was the perfect killer -- he was "The Terminator". Tamerlane killed for fun, he killed for profit and he killed out of principle. Tamerlane could single-handedly wipe out several platoons of elite soldiers entirely on his own, he was invincible in single combat, enemy leaders would flee with their entire armies at the mere offer of single combat with Timur. He and his armies could, and did, exterminate hundreds of thousands of people in days. Tamerlane was vastly more efficient and systematic as a killer than the Mongols or the Huns ever were. You see, Timur was a brilliant scholar of Muslim Shariah Law, and he could see clearly that few if any Muslims actually were able to live up the high standards set by the Koran. So, he realized that it was his sacred duty as a pious Muslim to exterminate them all. Needless to say, Christians, Jews, Buddhists, Hindus or, whatever, had to die as well. Timur's Empire encompassed Pakistan, Iran and Afghanistan, but, his campaigns stretched throughout Eurasia. He exterminated Russians, Poles, Mongols, Chinese, Indians, Egyptians, Syrians, Ottomans etc. And, it is in regard to this latter group that the main legacy of Timur -- other than significantly reducing the total size of the world's gene pool, of course -- is often thought to lie. True, all he really ever did was kill and steal, so his Empire collapsed instantly on his death, but, he also did something rather significant with regard to the Ottoman Empire, specifically. Timur crushed the Ottoman Turks so totally, that it actually took them half a century to recover. And, this may be quite significant from an historical point of view, because this probably delayed the conquest of Constantinople by half a century or so, and this delay may have been critical to the survival of Christian Western Europe. After all, Columbus discovered America just a few decades after the final Ottoman conquest of the Byzantine Empire, allowing the Ottomans to turn their energies West to the conquest of all of Europe. Without the wealth of the New World at their disposal, would the Christians of Europe have been able to resist the Ottomans? Wouldn't another half a century have been sufficient for the Ottoman Turks to have conquered all, or almost all of Western Europe? Quite possibly, it would have. On the other hand, we are assuming here a kind of "great man" model of world history. We are assuming that no "Columbus" could have occurred prior to the time that Columbus actually did discover America, OTL. In reality, Columbus was really following up the discoveries of Henry the Navigator of Portugal, who developed advanced shipping technologies for ocean travel in the Atlantic, in an effort to circumvent increasing Ottoman control of traditional European trade routes to India and China. If these pressures occur earlier, then we might well get an earlier Henry the Navigator, and an earlier Columbus. Hence, Timur's only impact in crushing the Ottoman Empire may have been delaying the discovery of America by fifty years, and its subsequent exploitation by Western Europeans. Thoughts?