I think they do:
Harrisongs wikipedia article.
Harrison's earlier songs for the Beatles are part of the Northern Songs package that Michael Jackson owned for a while, but Harrison hated the Northern Songs contract and set up his own publishing rights company before writing and recording songs like "Here Comes the Sun" with the Beatles.
Well, the rumors that Paul McCartney wrote the wong for him ... made me wonder.
Music Licensing is weird. I think all the large Venues buy ‘play rights’ from the RIAA