I haven't met a knitter yet that likes weaving in yarn tails, so teaching people how to do the Russian join is a technique I demonstrate whenever I get the chance. (Here's the tutorial.) I was recently teaching this method to a group of students at a fiber retreat when one person asked if the join works with cotton and cotton blend yarns. Great question!
The Short Answer
Yes and no. The Russian join can be done with cottons. Unfortunately, some of the things that make it work so well with wool and wool blends work against you with cotton yarns. But, with a little patience, practice and a couple helpful tricks, it can be done.