I just wanted to add my experience. I had braced on for 4 years. During which, all 4 wisdom teeth started growing in. After I got the braced off, my wisdom teeth continued to grow, pushing my newly straightened teeth back as almost crooked as they were to begin with. My dentist never told me to get them removed, but my orthodontist told me it might be a good idea. Well, I didn't have them out until only recently (actually 3 days ago). The whole time my wisdom teeth were coming in, I noticed my teeth shifting (I couldn't even wear my post-braces retainer, as my teeth were constantly moving and it didn't fit anymore.) My mom is mad that she spent $3,000 on my braces, and now they're crooked again. SO, I DEFININTELY think that wisdom teeth cause other teeth to move, even move dramatically. My teeth have been hurting off and on for years now (especially my front upper teeth), I guess when the wisdom teeth were pushing more against my other teeth. But now, since I have them out, I feel A LOT LESS pressure on my other teeth.
Just some 2 cents for you.