A peg-in-hole operation is representative of common tasks performed in assembly lines by robots. It requires registration of the coordinate frame where a part resides to the robot frame where it is acted upon. Poor registration causes misalignment of the peg and the hole which will result in a failed insertion of the peg. In this study, the dependence of the outcome of the insertion task on the quality of registration is investigated. It was shown in earlier studies that Restoring Rigid-Body Condition (RRBC) leads to decreased target registration error. This study quantifies the improvement in the Pass/Fail rate when the target registration error is reduced for a given peg-hole tolerance. A robot arm operated in position control mode was used to perform the insertion without performing any search algorithms or force/torque sensing. Results show that use of the RRBC method yielded substantial reduction in failed insertions, especially for tighter tolerances.