The short answer
In the sense Darwin meant, yes; in the sense most people mean, nobody knows. The edition was oversubscribed at the publisher's trade sale to booksellers on 22 November 1859, two days before publication.
The figures
John Murray printed 1,250 copies: 502 pages in one volume at fifteen shillings, with one folding diagram and no other picture. Twelve went to the author, forty-one to reviewers, five to Stationers' Hall, and about twenty more to Darwin for presentation, leaving about 1,170 for the trade.
At Murray's autumn trade sale the booksellers ordered about 1,500, and a large block went to Mudie's circulating library. So the edition was oversubscribed by some three hundred copies in a room of wholesalers, which is what Murray told Darwin, and what Darwin wrote in his diary: all copies sold first day.
Afterwards
A second edition of 3,000 followed on 7 January 1860. There were six editions in his lifetime, the last in 1872 at seven shillings and sixpence, reset in smaller type for a general readership. His last book, on earthworms, sold proportionately faster than the Origin had.