To be both pedantic and correct, there is no way to define a C function to restrict a string input so that it is correctly terminated. So no, it's at best documented that you shouldn't do that and definitely doesn't prevent you from doing this.
To be still more pedantic, there are two kinds of definition of an interface: definition-within-the-type-system and definition-within-the-documentation. The string library is specified in the ISO C standard (I use C99, but you can be all hip and C11 if you want), and passing an unterminated string to strcpy is a constraint violation.
7.1.1 A string is a contiguous sequence of characters terminated by and including the first null character.
7.21.2.3.2 The strcpy function copies the string pointed to by s2 (including the terminating null character) into the array pointed to by s1.
Therefore, code which passes an unterminated string to strcpy is not conforming code (because s2 does not point to a "string" as C99 defines it).
Of course, you should use strncpy anyway. But that's not the point.
