\0 will be interpreted as an octal escape sequence if it is followed by other digits, so \00 will be interpreted as a single character. (\0 is technically an octal escape sequence as well, at least in C).
The way you're doing it:
std::string ("0\0" "0", 3) // String concatenation
works because this version of the constructor takes a char array; if you try to just pass "0\0" "0" as a const char*, it will treat it as a C string and only copy everything up until the null character.
Here is a list of escape sequences.