I don' t think there is any connection.I wouldn't have thought Fleming would have based an inventor of gadgets on a literary critic and novelist. Q as a person isn't mentioned much in the books he only comes into his own in the films.
Q is I think for for Quartermaster.. He is the head of Q Branch, the research department of the Secret Service.
Quiller Couch just used Q as a pen name.His given name was Arthur Thomas Quiller-Couch.
shaney is right. Q stood for Quartermaster. His real name is Major Boothroyd (as mentioned in Dr No)
However.............................. just to throw a spanner in the works, John Cleese was refered to as "R" in The World is Not Enough"...................
And................"M" was supposed to stand for Minister. However, in Casino Royale we learn that M is the initial of Judy Denches character. Confusing..................
Fleming named Major Boothroyd after a man called Geoffrey Boothroyd who corresponded with him about the armaments used in the early books.
M in the Fleming novels was Admiral Sir Miles Messervey.