There have been several studies on this issue. The results are inconclusive. It seems that not everyone with ACL injuries or repairs has the type of changes you describe. For those who do, several studies show improved sense of joint position after wearing knee supports. Other studies show no difference after bracing.
A rehabilitation program is more likely to be beneficial. There are specific exercises physical therapists use to help improve the joint's sense of position. If your knee feels unsteady (as if it might give out from underneath you), these exercises can still help. Check with your physical therapist about this.