Does Islam as we know it exist in Supernatural?

In Islam, jinn (demons that can be good or evil, Muslims/Christians/Jewish people or disbelievers) were created and populated the earth before humans. They are the first to enjoy free will, but because of their mischief and wars God ordered angels to destroy them, except some who had taking refuge in remote islands and mountains. Azazel, a devote demon that was elevate to the rank of the chief of angels in the lowest heaven was also spared. Angels have no will so technically Azazel/Lucifer cannot rebel.

Then god decided to populate the earth again with man, and ordered angels to bow before his new, best creation. Azazel rebelled because of his free will, and because he was created from pure fire he sees himself as superior and so does not want to bow before a creation of clay. So God damned him and named Him Iblis the Shaytan. (Shayateen are the plural of shaytan or Satan the evil demon or evil jinn or typical western demon) Iblis means rebel, so he was damned to hell for his public disobedience.

Instead of demanding mercy he asked to live until the day of judgment. He will then take revenge on those he blames for his fate: mankind. He trapped Adam by getting him out of heaven, and he seduced mankind and led them to hell except the devoted men of God. So there are no battles in heaven, and Satan only challenges God by destroying the religions of the messengers.

He leads men to Idolatry, witchcraft, disbelief, and Satanism, and brings to the world his final challenge. This is the coming of the Antichrist, the one eyed man (only described in Islam). Islam has no use in this show. This is because the rules are solid and the only formidable facts that can be use in cinematography are the last day on earth or the Islamic Apocalypse. These may be used in another series, but here the Christian ones are being used now. The Ghuls and Jinns are used from Arabic civilization, however.

I tend to take an additive view for most TV shows and movies. That is, I'm inclined to believe that everything which exists in our world also exists in their world, unless explicitly contradicted by the show's canon. (Except for the actors who portray the characters, of course. I'm inclined to think they do not exist down in Hollywood, unless the show's canon establishes that they do.)

Is there anything in Supernatural that refers to Islam further, whether it be for or against its existence?

As for Islam, it has been well established that the "real story" of the world is closer to Judeo-Christian myth than any other, but I'm inclined to believe Islam still exists as a religion which human beings follow in some parts of the world. I certainly haven't seen anything in the show that explicitly denies the existence of Islamic faith. It may not be literally true, but even their interpretation of Judeo-Christian mythology is not 100% accurate (likely on purpose.)

Granted Islam is not a big part of the show, but that doesn't mean it doesn't exist. They also don't mention buddhism, taoism or any of a myriad other religions that are practiced around the world in our reality. In fact, aside from the Judeo-Christian faith, the only other religions that tend to get mentioned with any serious content behind them are the pagan religions of antiquity, in connection to the "pagan gods" they occasionally stumble across.