We have a good stockpile of info on these pieces in our archives available through Search . The case style and inscription are indicative of the counterfeit pieces that vexed V&C from 1850 onwards. Without seeing the movement, I can tell you it can't be pre-Constantin as 1) they did not have cylinder escapements, and 2) they did not have 5-digit serial numbers. Again, a movement photo would complete the story.
There is an entire family of collectible watches known as the "Swiss Fakes" that were made to copy American watches, and this practice carried over to the better known Swiss brands. The Swiss decentralized system of production made it very easy to scribe any name on your anonymous watch that would increase its value. Some of them were very nice, I'm sure the Christie's piece was good quality, but not genuine V&C (nor did Christie's claim it was). Note the date of 1860 in the listing description! It is what it is.
Here is a short history of the brand for our original poster; between 1755 and 1785, the first watches appeared in Geneva under the name "J.M. Vacheron à Genève" for Jean-Marc Vacheron. His sons Louis Andre and Abraham followed. Pieces signed "Louis André Vacheron" appeared briefly, but it was the younger son that carried on their father's legacy commencing in 1785 with watches signed "Abraham Vacheron". That was to change a year later in 1786 with the introduction of a new partner and the signature"Abraham Vacheron Girod". These watches were numbered 5000 and 6000 range. Beginning in 1819, all pieces were signed with the familiar "Vacheron & Constantin".