I think BJ is correct. Matt Jefferies was interviewed and he is asked about NCC-1701 at the 5:18 mark. He didn't get the plane until after TOS went off the air and claimed it was not the source of the numbering.
However, he does confirm (or re-confirm) that the numbers were picked to be easily recognizable and it was the 17th design and the 1st bird, etc.
Interestingly, by his thinking, the Constellation being the 10th design would suggest the basic saucer + secondary hull + nacelles had been around for a long time