Not to derail this thread, but I think you can... if you have an elite coach. Petrino did very well at Arkansas and they weren't exactly setting the world on fire with recruiting. South Carolina has been the second or third best team in the SEC over the last three years without top rated classes (although Spurrier's clearly landed a few elite recruits along the way). With some notable exceptions (e.g., Clowney), Dooley arguably recruited at a similar level to both of them, from a simple Rivals rating standpoint.
But, regardless - Dooley clearly was not an elite coach, so he wasn't helping himself by not always signing elite talent.
Did Petrino or Spurrier ever come close to winning the SEC at Arkansas or USCe?
