"Do you think a transfer student would have access to composition classes at Thornton at USC? "
yes. They do not reserve comp classes for those who have gone to USC since their freshman year. USC accepts about 1000(!) transfer students a year.
"Do they allow non-majors to take composition classes? "
yes.
see the link below
"Below is a list of courses that USC students, both music majors and students from other programs, may take as electives or as part of a music minor. "
https://music.usc.edu/departments/minors-and-electives/electives/
here are other links regarding admissions deadlines for submission of music materials for those wishing to apply to the music program as either a freshman or transfer student
- THESE DATES ARE EARLIER than the normal USC admissions deadlines.
. http://music.usc.edu/admission/minors/
https://music.usc.edu/admission/deadlines/
here is a link to the USC catalog
http://catalogue.usc.edu/index.php?catoid=2