Customer service experience can actually be pretty helpful. Just play up any responsibilities or skills that you developed that could be applicable to scribing (e.g., working in a fast-paced environment, adaptability to many different situations, etc.).
I'm a chief scribe for one of the big scribe companies, and I'll be honest, a lack of clinical experience could hold you back. I don't think it's a nail in the coffin though, and it may not even matter depending on what kind of site you work in (big vs. small, outpatient vs. ER) and how much training they are able or willing to provide. Definitely include evidence that you know basic medical terminology and can type >65 wpm at least.
Keep in mind that shadowing and volunteering count for clinical experience (for scribing, at least), so if you have those, definitely include them! It shows that you've had at least some exposure to the medical field.