Absolutely. While the cello has a long classical tradition, it's a remarkably versatile instrument that shows up across a huge range of genres. Folk and Celtic music have deep roots with the cello. Jazz cellists like Ron Carter and David Darling have built entire careers outside the classical world. And in rock and pop, the cello has had a presence from the Beatles to Apocalyptica to Yo-Yo Ma's genre-crossing collaborations.
That said, most beginner method books and early instruction are rooted in classical technique — and that's not a bad thing. Classical training builds a strong foundation in tone production, intonation, and bow control that transfers well to any style. Many non-classical cellists got their start in classical study before branching out.
If you have a specific style in mind, mention it to your teacher from the beginning. A good teacher will incorporate your interests into your learning, introducing style-appropriate repertoire and techniques as soon as your foundation allows. Some teachers specialize in non-classical styles entirely, so if folk, jazz, or rock cello is your primary goal, it's worth looking for someone with experience in that area.
The cello's rich, warm tone makes it a natural fit for almost any musical context. Whatever style draws you to the instrument, there's a path to get you there.