There is no scientific evidence to support the use of a bra to prevent sagging. Best of luck with your reduction.
For most women wearing a bra on a day to day basis is helpful to slow the sagging process. This is more important with larger/heavier breasts and less important with women who are an A cup. The supporting tissues/structures of the breast cannot over a long period of time resist the weight and pull of gravity for larger heavier breasts. During the day most women are upright and the pull of gravity stresses and strains the supporting structures of the beasts. Over the course of a few years (or less for heavier breasted women) this constant pull will cause stretching of the skin and supporting ligaments of the breast leading to sag. Wearing a bra transfers the load to the bra and the shoulders so that the breast tissues are not strained. This will definitely slow the sagging process down
In the long scheme of things we cannot really defeat aging, gravity or death. The largest and perkiest breasts of one's 20's frequently become the sagging breasts of one's 50's and older. The only way to slow Gravity is by having support (i.e. A bra) while upright and avoid activities which result in skin aging (tanning, smoking etc). I really think wearing a bra while sleeping is a bit of overkill but it may be useful for the very large breasted women to decrease lateral displacement and stretching.
As regards lactation and any breast surgery consider that the milk ducts are not sterile and cutting across them especially when you are actively lactating increased the infection rate. Secondly, a breast which is lactating is larger than the non-lactating Breast. So reducing or augmenting a temporarily larger breast builds in an avoidable error which would result in breast sagging once you stop lactating.
Dr. Peter A. Aldea