When I create a std::string using the default constructor, is ANY memory allocated on the heap? I\'m hoping the answer does not depend on the implementation and
Generally, yes they allocate memory on the heap. I'll give an example: c_str() requires a NULL trailing character '\0'. Most implementations allocate this NUL \0 ahead of time, as part of the string. So you'll get at least one byte allocated, often more.
If you really need specific behavior I'd advise writing your own class. Buffer/string classes are not that hard to write.