Tom and Tony
Certainly Darwin was a good friend of Colt, and Alison, and Low and Croome and Fowler and Simpson and Campbell (who was a 'roving' reporter for Darwin for a while) and Hutchison. I'm sure he knew every architect working in England. As Bob says below, many of them were O&CGS members. I have never heard of Mackenzie being a member of that golfing society though.
Mackenzie is referenced in a number of Darwin's writings, quite extensively in his 1925 update edition "The Golf Courses of Great Britain" and the various editions of "A Round of Golf on the LNER". Darwin writes in two different articles in Country Life of just having met with his friend Dr Mackenzie, who no doubt got some good publicity out of Darwin's articles on his Australian Tour and his Cypress Point course (thanks to Tom MacWood for those articles).
So my suggestion Darwin put forward Mackenzie to CBGC is just speculation on my part and he could have just as easily recommended Colt or Alison or no-one at all. By 1924 when Mac was beginning his work at CBGC, his partnership with Colt and Alison had been dissolved. Its possible that Mac knew Doyle, but Darwin definiely would have and darwin knew Mac, that was all I was suggesting. The Secretary at CBGC was Frank Holroyd who was a friend of Mackenzie and so of course it is possible that Holroyd was the man who got Mac on board there, with no involvement of Doyle. I am not aware of any specific instances where Darwin recommended an architect, and if he did so, I'm sure he covered his tracks so the others he knew did not get upset with him.
Darwin wrote a number of golf club handbooks for various clubs, but he was by no means as prolific as Robert H K Browning or Tom Scott. So far I know of around 60 clubs that Darwin wrote the course description sections of their handbooks. He almost certainly would have been paid to do these, while he may have done one or two as a favour, possibly for clubs such as Woking and Worplesdon. Darwin was a member of numerous golf clubs and if he did a favour for all of these he would have been busy indeed working for nothing.
Bob
CD would have known Darwin through the Strand magazine, not Mackenzie.