I guessed no, but this output of something like this shows it does
string s=\"\";
cout<<&s;
what is the point of having empty string
If there truly was no point to the empty string, then the programmer would not write the instruction at all. The language is loyal and trusting! And will never assume memory you allocate to be "wasted". Even if you are lost and heading over a cliff, it will hold your hand to the bitter end.
I think it'd be interesting to know, just as a curiosity though, that if you create a variable that isn't 'used' later, such as your empty string, the compiler may very well optimize it away so it incurs no cost to begin with. I guess compilers aren't as trusting...