Does the head of a pump depend on pipe diameter?
What you are looking at is really just the static lift height. The Total Dynamic Head (TDH) is what you need to look at when sizing a pump. For a well pump, to simplify:

TDH = Static Lift Head + Pressure Head + Friction Loss


So to answer your question: pipe diameter directly affects friction loss, which largely influences TDH. 

You can get charts that show friction loss for different materials of pipes (I can only find ones on commercial sites so I won't link them), but the smaller the pipe, the higher the friction loss. Fittings also introduce friction loss, and there are charts that show equivalent distance each fitting adds (for example, a 1" elbow is equivalent to +7' of pipe). 

As an example of how diameter affects TDH, to get 12 GPM with 200' of pipe with a vertical rise of 80':

Diameter     TDH
--------     ---
3/4"         159'
1"           99'
1 1/2"       83'
2"           81'


There are many TDH calculators that simplify all of this (again, I won't link since I can only find commercial sites), and that's the easy way to figure this out.