When we ordered mail-order transplant plugs, we broke apart the rootballs of half of the plants that were seriously rootbound, a practice that is often recommended. The other half we left alone. In all cases, the plugs whose roots were left intact grew better than the ones that were split open or untangled.
We talked to several transplant experts, including Michael Orzolek at Pennsylvania State and Albert Liptay at the University of Guelph in Ontario, about our observations, and they weren't surprised. Liptay has studied the tendency of roots to circle around the sides of containers rather than growing all through the soil mass (the roots follow the path of least resistance and seek the high oxygen environment at the edge of the rootball). He says that, when transplanted, annual vegetables and flowers can quickly generate new growing points all along the roots at the edge of the rootball, and will begin exploring the new garden soil almost immediately if the ground is moist and in good contact with the rootbound mass. Untangling may be a good idea for shrubs and trees, which have permanent roots that may choke each other as they expand over the years, but for annuals it only slows the plant down.