A rotary propulsion system for a tiltrotor aircraft operable to transition between rotary and non rotary flight modes. The rotary propulsion system includes an engine coupled to a freewheeling unit. A gear system positioned between the freewheeling unit and a proprotor assembly has a torque path coupling assembly disposed between an engine side gear assembly and a rotor side gear assembly. In a disengaged position, the torque path coupling assembly interrupts the torque path between the engine and the proprotor assembly. In an engaged position, the torque path coupling assembly completes the torque path between the engine and the proprotor assembly. A hybrid power unit is configured to accelerate the engine side gear assembly to match the output rotating speed to the input rotating speed enabling the torque path coupling assembly to shift from the disengaged position to the engaged position.