Nat Pendleton, Admirer Of June
"Jim Driscoll" is mentioned a few times in Plexus as being one of June's admirers:
"Jim Driscoll, whom I have seen in the ring, is a wrestler with intellectual pretentions." (p. 394)
"[Arthur Raymond's] idol was Jim Driscoll, who had lately turned professional. Perhaps it was because Jim Driscoll had once studied to be an organist that he adored him so." (p. 406)
"Another [who lavished attention upon June] was the wrestler, Jim Driscoll." (p.591)
I've found no evidence on the internet that Pendleton studied the organ, but, according to this biography of Pendleton, he spoke several dialects and was not at all the dumb lug he was often portrayed as on film (see his filmography here; Pendleton [at left] as Eugen Sandow from The Great Ziegfeld, 1936 -- taken from this website).
Pendleton was born in Iowa but came to New York to study and begin his wrestling career. In 1920, he competed as a wrestler for the U.S. Olympic team and came home with a silver medal. He became a popular pro wrestler, which led to a few supporting roles in feature films in the mid-to-late 1920s, when June was hanging out with him. As Ferguson says in his book: "Pendleton had lately been having some success in films as a 'heavy,' and June may have hoped that he could help further her own acting career." (Henry Miller: A Life, p.144).
Ferguson also relates a story of Miller spying on June and Pendleton and then confronting his wife about the affair, similar to the incident depicted on page 9 of Nexus.
Miller likely fictionalized his name as "Jim" in honour of a Greek wrestler Miller admired called Jim Londos. Miller wrote about Londos in one of his earilest written sketches (a mezzotint I think).