The scholarly paper "Do Lawyers Really Believe Their Own Hype and Should They: A Natural Experiment," says "yes" and "no". The conclusion is based on evidence that students in moot court competitions "overwhelmingly perceive that the legal merits favor the side that they were randomly assigned to represent," even after the competition is over. The authors Zev J. Eigen of Northwestern University School of Law and Yair Listokin of Yale Law School, also found that overconfidence is associated with poorer performance in advocacy as measured by legal writing instructors. Unlike a previous study, these authors found no gender effect. (See Lawyers' Ability to Predict Case Outcomes: Study Suggests Gender Differences).
The paper includes the interesting caution that the overconfidence caused by the act of representation can have an important effect on a lawyer's ability to settle a case:
When both sides' lawyers perceive their cases as high probability winners, they are less likely to settle and may be less likely to prevail upon their clients to settle. The impact of representation on confidence also offers a cautionary tale to lawyers considering a practice area in which they do not agree with their clients -- merely practicing in the area is likely to shade the lawyer's views on the legal and moral merits of the issues.