According to me, they should not because negative of work done by external agent = change in potential energy and since, due the absence of external forces, total energy remains conserved therefore, kinetic energy of system should also remain the same.
The work done by the internal forces can increase the kinetic energy of the body. In accordance to work-energy theorem, the net work done by the forces acting on a body is equal to the change in the kinetic energy of the body. The work done by internal forces will increase the internal energy of a body. The increase of internal energy of the body results, its constituent atoms or molecules might acquire this energy in several different forms like increase of translational kinetic energy and increase of rotational kinetic energy. Therefore, the work done by the internal forces can increase the kinetic energy of the body
For sure internal forces cause a change in the potential energy of the system. But as for kinetic energy, it may or may not change it. For example, consider a ball raised to a height h above the ground slowly, (considering our system is the earth and the ball), the ball gains potential energy and all the mechanical energy gained is potential. Ok then when it is falling down it will have both changes in kinetic and potential energy.