Yes and no...
Depends on where you live, and the source of the material that you are using. For the most part termite colonies and carpenter ants are not going to invade an ares with chips to make colonies. They prefer logs and larger size wood. Now, that being said, chips are cellulose debris, and that does attract bugs that eat wood. They home in on it. So keep it from coming into contact with the house and barn siding, etc.
As for keeping down the mud, it works great. I use chipper material for paths around here, in the gardens, fields, etc. Wood and bark debris, small branches, etc. I only use material that I have cut and chipped here on the property. That is becasue of disease and invasive weed seed. If you chip a tree with fingus, you are going to spread that fungus all around your property. Non-wood-eating bugs, fungus, and other diseases love a free ride to a new source of plants to dine on and invade. In central CA, Sudden Oak Death (fungis) is a huge issue, and I would not recommend getting any chipper stuff in an area like that. Here we have several forest types of bugs and disease (ie., Port Ordord cedar disease). An issue with chipped invasive shrubs like large Scotch/Portugese brooms is that you may plant a lot of seeds in the chipper material if that stuff is in there.