Yes, cotton shrinks, andthat goes for cotton batting as well as cotton fabric and cotton thread. Usually they all shrink nicely together, and not by very much. Batting manufacturers put the percentage of shrinkage on their labels-- usually 2-5%.
I've been making quilts since 1969 and I've made hundreds and hundreds of quilts. They've all been quilted with cotton thread, and I've never had a problem. Most were hand quilted, many were machine quilted.
I use miles and miles of cotton thread. I've been a longarm quilter for the last 5 years, and I buy 6000 yds of a color at a time, 108 colors in stock at all times. I'm a threadaholic.