Maybe there is a link. There is some facts both for and against this.
There is an earlier response in this thread from Frances concerning William and Ann. They also had a child called George.
Now I currently suspect that my George Duncan's father was also called George (you can find him on the 1841 census) which hints at being the name of William's father.
Much of the above is based on no more than hunches and circumstantial evidence.
The one thing that maybe suggests no link is that I believe George to be a Civil Engineer and is listed in some places as a gentleman. William is listed as tradesman living at one time in the 'House of Industry' which I believe is 'social housing'. This doesn't, on the face of it, tie up, but who knows what goes on within families.
I am going to try and get a copy of the will for the older George Duncan which I'm hoping will shed some light on his offspring. I'll let you know when/if I find anything out.
Richard