Is there an original copy of the Koran?

In the same way that there is no original copy of the Bible, there is no original copy of the Koran. In some ways that is surprising, insofar as it is the work of one man and a few scribes, whereas the Bible is probably the work of hundreds. It was written over many years. 

There seems little doubt that it was revised, edited, rewritten, re-revised many times during it's inception (otherwise why would such a (comparatively) short book have taken so long?

There is an original copy of the Koran in the chest of every Muslim who memorizes it. We see that all Muslims unlike others, never differ about the chapters of the Koran or its verses or its words or its accents or even its letters. The Koran memorized by an Arab Muslims is the same Koran memorized by an Indian or a Persian or a European or an American or a Russian or any other Muslim. Besides, the authentic copy of the noble Koran collected by our sir Abu-Bakr and put at the house of lady Hafsa daughter of Omar Ibn-Al-Khattab, was taken by our sir Othman and he made four copies and sent them to different parts of the Muslim nation of his time. 

The copy sent to Egypt is still kept in the Islamic museum at Bab El-Khalk in Cairo and it is called "The Mos-haf of Othman". There is another copy kept in the museum of prophetic remains in Astana in Turkey. They are the authentic copies from which are written and printed all the copies of the Koran until now.

What difference would it make if there were an original copy of this delusion? Why would anyone care?

Now to have an original copy of The Origin Of Species By means Of Natural Selection, Or The Preservation Of Favored Races In The Struggle For Life would be having something!