I think it's possible for somebody with ASD to have no particular special interest, certainly for a time, though I suppose it's rare. I think special interests are just things that often happen as a result of something more primary that's going on in the brain, but they don't necessarily always happen all the time. That primary something may be a strong tendency to focus on detail and a deeply gratifying sense of satisfaction from really looking at something in depth.
I've certainly had special interests, and potentially I still do, though currently my day-to-day behaviour isn't really showing any particular subject or activity as a special interest. In a way I wish it would, because I get a lot of pleasure out of getting obsessed with a subject and developing my skills and expertise in it, and I tend to get morbid and bored without such a thing to exercise my brain.
Having said that, I'm not perfectly happy while immersed in a special interest, because I'm aware of how being too immersed in such an interest can impact badly on the rest of my life, so I can't really indulge without also feeling a degree of nagging anxiety that I'm living the life of the Nowhere Man in the movie Yellow Submarine, lost in an analytical world that's ultimately extremely lonely and a rather pitiful waste of my life. There's always been a conflict in me between special interests and social needs, and the time when I was happiest was when I hardly bothered with special interests at all because I was lucky enough to be surrounded by people of a kind I could really relate to, so I spent nearly all my time in their company.
Even then I wasn't perfectly happy, because it would annoy me that the almost constant presence of friends in my life meant that I "couldn't get anything done." It must be great to be able to strike a balance between social activities and lone special interests, perhaps even fusing the two together by sharing special interests with others who feel the same fascination, but I was never able to find people who were fascinated by exactly the same things that fascinated me, and I was never able to find a "switch" I could throw at will in order to go from social to special interest and back.