An preliminary report published in 1990 suggested that Wide Abdominal Rectus Plication (aka the WARP abdominoplasty technique) produced some back pain relief in 24/25 patients treated.
However, this has not been substantiated and should not be the primary reason you seek abdominoplasty.
Furthermore, most insurance companies do not accept this as in indication for benefits coverage.
If i can explain. Your spine depends on a delicate balance between your stomach muscles and back muscles. When your stomach muscles are weak you may have an abnormal posture which creates excessive back discomfort.
Think about how it feels on your back when you have been sitting "Indian-style" for a while.
This is the reason orthopedic surgeons and spine surgeons will often prescribe a course of physical therapy to strengthen your abodminal muscles. It is also why Pilates and Yoga core strengthening exercises can improve minor back pain. I perform Pilates after a long week of surgery and I find dramatic relief from back strain.
The muscle rearrangement that occurs with abdominoplasty can enable you to use these stomach muscles in a more normal fashion and improve back pain but it should not be the sole reason you seek surgery.
In fact, in the early postoperative period, you may experience a greater degree of back pain you feel due to excessive bending forward from your tendency ot releive the pull felt by tightening the skin.
I hope this helps!