Dear Carrie,
There's no way to tell how long it will take to see progress. Sensory integration problems take on many and varied dimensions with ranges of severity.
Disruptive behavior is often associated with sensory integration problems, but isn't diagnostic of such problems. In other words, it may be useful to consider additional evaluation/intervention re: the disruptive behavior (depending on the nature of the disruption).
Surely talk with your daughter's teachers about the matter of her readiness for first grade. You already know that she requires some specialized intervention. Will this be sufficient to allow her to proceed in the regular first grade classroom? Time will tell, but see what the teachers and specialists think.
Here is a book that many of my friends recommend. My children do have have any SI issues but I have heard them praise this book.
The Out-of-Sync Child: Recognizing and Coping with Sensory Integration Dysfunction
By Carol Stock Kranowitz
Format: Paperback, 1st ed., 352pp.
ISBN: 0399523863
Publisher: Berkley Publishing Group
Pub. Date: February 1998