The Mysteries of Udolpho and James Henry's The Turning of the Screw, I'd say it's closer to the later. For most of the book, the supernatural aspect is not that strong and it could easily be the product of paranoid minds. Only in the last few chapters does the supernatural aspect come out very strongly.
Now, it took me a little while before I understood what the book was about, so here's a really quick summary. It's 1905 and Woodrow Wilson is the president of Princeton University. He's really convinced that he's rival Andrew West is out to get him. Cue scene change to the Slade Family, as a paranormal activity (one of the Slade girls gets abducted) sets a chain of paranormal events (or just highly unusual events that are ascribed to the paranormal), which is why the book then jumps around from inhabitant to inhabitant. Which makes it sound rather ghostly, as though it was possessing the different characters.
Another thing the novel reminded me of was a novel from Wilkie Collins was the style of writing. There wasn't just multiple perspectives, there were multiple narrative styles. Some, like journal entries, were harder to read than others (because they did not make sense at first).
But still, this is a riveting novel. The more I read it, the more drawn into the novel I was. I admit that I didn't really care for the characters at first, but by the end of the novel, I think that even if I didn't love them, I could understand their position. For example, Uptown Sinclair, the guy that wrote The Jungle (I should really read that too). At first, he seemed like a pompous guy who was too happy to make his wife suffer for his ideals. But as I read on, well, I didn't become a fan, but I did find him rather sympathetic - he was a complete idealist, and the real world isn't kind to idealists like him.
What helped me through this novel was actually Wikipedia. Once I got a sense of who the characters were (this may not be necessary for you if you're familiar with American history), understanding and enjoying the book became a lot easier.
Note: I read this book as part of the Tea and Books reading challenge.