No. String theory's resolution of the old paradox is a sign of the hidden cleverness of string theory.
After he read some of my essays on the electron's spin, Tom W. Larkin asked an interesting question:
Does string theory resolve the paradox of (post-)classical physics that the electron, if imagined as a spinning ball of a very small radius, has to rotate faster than the speed of light for its spin to be \(\hbar/2\)?One natural, fast, legitimate, but cheap reaction is to say: the electron isn't really a rotating ball. The spin may be carried even by a point-like particle, without any violations of relativity, as QED shows, so the paradox has never been there.
Of course that a string theorist is likely to answer in this way, too. Quantum field theory is a limit of string theory so any explanation that was OK within quantum field theory may be said to be correct within string theory, too. The paradox doesn't exist because the electron isn't a classical ball that gets the mass from the electrostatic self-interaction energy.
However, string theory does represent the electron (and other elementary particles) as some kind of an extended object which is qualitatively analogous to the rotating ball so some version of the "superluminal spinning" paradox may be said to reemerge in string theory. Does it cause inconsistencies within string theory?