It can't be straightened completely since the upper storeys were built askew to compensate for leaning that occured during construction.
What do you know, just last night on one of the Discovery channels (Discovery-Science I think) they had a program about the project to save the tower.. very interesting. You are right, they dont intend to(nor could they) straighten it out completely, They'll leave it leaning, just a bit less than it has been the last several decades. They want to keep it at a "safe" lean, one where they can allow visitors to the interior. They are, basically, slowly sucking out dirt from underneath the "high" side, allowing the ground to settle down and thus righting the structure (a bit).