No, why do you think that would be the case? Whether you convince your interviewers that you're passionate is entirely a function of how much thought you've given to your motivations and how well you articulate yourself -- there is no intrinsic 'passion for medicine' that doing a science degree automatically confers on you.
Similar to the above -- interviewers and med school staff recognise that applicants come from a wide variety of backgrounds and welcome this diversity rather than being apprehensive of it. In fact, an applicant who's completed an entirely unrelated degree like law or the humanities, and is able to articulate their reasons for deciding to switch paths, will probably strike the interviewers as more well-rounded and mature than someone following the comparatively more run-of-the-mill science-to-medicine pathway.