Throughout the principle films (not so much in the extended series), Pinhead gives awesome and well-written diatribes on pain, humanity, suffering, the meaning of pleasure and pain; his teachings, beautiful words and priestly demeanor are what make the films. The demonology of Hellraiser 1, 2 and Hellraiser: Inferno is interesting and unique.
The films are about indulgence. If you indulge, without foresight and without restraint, you will destroy yourself, and the cenobites are the tools of that destruction, and the methods by which you learn that it is true: Human desire has sensible restraints that shouldn't be crossed!
The Church of Satan states that "Satan represents indulgence, instead of abstinence!" as its First Satanic Statement. In this respect, pinhead and the desires that unleash him are Satanic. But, the sensible pro-Human refrain to the First Satanic Statement is "the difference between indulgence and compulsion. Indulgence can be controlled, compulsion controls". Hellraiser is the story of people who cross this line and destroy themselves and those around them. Satanism, along with the teachings of pinhead on desire, are the portals through which we can learn where these lines of self-destruction are, and learn to stay within them for maximum indulgence combined with a graceful life, as opposed to self-destruction.
If I was a character in the film, I don't see myself as pinhead, but as one of the Human demonologists who, throughout the series, are found studying pinhead and who dream of the box.