What Colin said.
When Madonna was seeing Sean Penn one night while he was sleeping she got upset with him and dripped CA in his crotch..... He awoke and was all....... glued together. The story got out because he had to go the the ER where they used CA debonder (acetone) to undo the damage. So yes CA will work fine on things like nuts......
but staining may be an issue.To glue my guitar nuts.... on I simply use the smallest drop of Titebond applied with a tooth pick under the nut and on the face of the nut that will contact the end of the fret board. This way when I want to remove the nut just a light tonk with a wooden block and a fret hammer and the nut comes loose.
The use of a wooden block and a little hammer technique comes from Frank Ford.