In the long run, straightening the teeth can help you clean the teeth much better which can be a great benefit if you are predisposed to periodontal disease. You must get the periodontal disease under control before you begin any orthodontic treatment!!!! Periodontally infected teeth will move really well - you may even move them out of your head! OK, maybe that wasn't funny to non-dentists, but you get the idea. Orthodontic forces will erode infected bone in a hurry.
Another facet of this is the effect the bite can have on periodontal disease. For some strange reason this is ignored by most dentists and periodontists. Teeth which have bite issues tend to be the worst teeth in any periodontal case. It's not a coincidence!!!