Are you kidding me Davo?
The Cure was one of THE archetypal Goth bands. You could even say that Robert Smith was one of the earliest Emos.
But you shouldn't overlook the tangental influence into Goth culture from people like Ozzy Osbourne, Alice Cooper and that whole death metal, theatrical rock movement. There are other influences on the Goth movement and indeed The Cure too. From the punk world, there are bands like the Theatre of Hate. From the comics and mythic worlds, there are also the vampire genres. From philosophy, there are all the existentialists.
For sure, The Cure were a slightly softened, late 70s-early 80s, poppy version of all these influences, but their work saw all this culminating into some early sense of what it was to be a Goth.
They were definitely a Goth band more than a Pop band, in my book at least.