Will my jawline and chin sagging worsen after Smart Lipo?

I am scheduled to have Smart Lipo along my jaw line and under my chin. I am very thin and do not need to have fat removed. The elasticity of my skin is not great and I have slight jowls and verticle bands pulling on my neck. My surgeon says Smart Lipo was made for cases just like mine. I am concerned after reading some of the comments that it could actually make my drooping skin problem worse. I am also concerned about the physician comment about the vascularization of the skin being compromised. I am 54 years old, fit and in good health.