It is not known if they had any contact in the intervening decades, although both taught English at the University of Wisconsin in the mid 1930s.
During WW2 Hayakawa taught at the Illinois Institute of Technology in Chicago. He was a colleague there of Moholy’s friend and fellow Hungarian Gyorgy Kepes.3 When Hayakawa took courses at the near-by Institute of Design, perhaps introduced by Kepes, he became friends with Moholy-Nagy — a friendship he described for a University of California oral history project.
McLuhan certainly heard of Moholy-Nagy from Giedion. He reviewed Moholy’s 1947 Vision in Motion together with Giedion’s 1948 Mechanization Takes Command in 1949. But it is conceivable that he also heard of Moholy-Nagy from Hayakawa (if, say, they were keeping up with each other at meetings in the 1940s). Inversely, since Hayakawa and Giedion both contributed to Kepes’ 1944 The Language of Vision,3 and since that common appearance may have reflected some kind of acquaintance between the two, McLuhan may have heard something of Hayakawa, his old neighbor, from Giedion, his new mentor.