You can specialize in any era you want without knowing Latin. From what I can tell, many of our flairs here do not have the language, and the general academic standard of latinity, even among advanced degree holders, is shockingly bad. This is particularly true for those who study fields traditionally thought to be based in the vernacular, such as later Insular and French culture or the Italian renaissance.

EDIT: As this point seems to require clarification, there is surprisingly very little emphasis on Latin, even in fields which would seem to require it, at almost every level of historical practice.

Whether or not you believe that this general inability produces worse scholarship (clearly, I do), those scholars generally considered at the top of their fields for periods before ca. 1400 possess fairly impeccable Latin almost as a rule, along with knowledge of at least 3 other modern languages (French, German, English). Once you get into the Early Modern period, Latin becomes less important, but this is because many early modernists tend to ignore it (a constant source of frustration for some of us). After the 18th century, there is very little need for it.