Yes, it is possible (in the US, at least). You need to get hired, so you need to meet the needs of a faculty position, both in teaching and research, but having an interdisciplinary degree doesn't rule that out.
Some places will be more receptive to the idea than others. Some universities value cross discipline collaboration and have, say, undergraduate programs that value cross discipline study. Applications of CS to other fields is fairly popular, though not universal.
Some large faculties have a few members who have quite diverse interests.
But, a person would likely have fewer opportunities with any degree that isn't, somehow, mainstream.
And, you also need to be able to earn tenure if you want a career. And once you do, you have the opportunity to expand diverse interests in the institution.