Naval tradition holds that the class takes the name from the lead ship of that class. Given Gene's service in the U.S. Navy, you can easily extrapolate that the tradition followed him into Star Fleet.
As such, I would consider the lead ship of any class mentioned in the show to be canon. I don't recall ever seeing a USS Galaxy on screen, but does anyone deny that the Galaxy exists in the Star Trek Universe?
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz