@JonathanBeardsley If by simplicial categories you mean simplicially enriched categories we had this discussion a few days ago. Bottom line: yes, but probably not in a way that forms a simplicial model category,
If you meant functors from \Delta^{op} to categories, ignore everything I said
I can't imagine that simplicially-internal categories are so different from simplicially-enriched categories in this regard. Is there any model structure on simplicially-internal categories which presents (\infty,1)-categories?
Or even a model structure equivalent to (incomplete) segal spaces for a start?
Fun fact: that simplicially enriched categories can't be a simplicial model category was the original motivation for considering complete Segal spaces.
