A non-business background does not automatically hurt you. Firms routinely interview candidates from science, medicine, law, and other fields. The key question is whether you can think in a structured, business-relevant way during the interview.
That means you do need to understand some basic commercial language and concepts. You do not need to arrive sounding like a consultant already, but you do need to interpret the case with sound judgment and show that you can learn quickly.
So yes, casing matters a lot, but so does building enough business intuition that your answers do not feel detached from how companies actually operate.