Answer
The statement is false.
Work Step by Step
The work-energy theorem states that $$W=\frac{1}{2}m(v_f^2-v_0^2)$$ $W$ is the work done by a net external force on the object
In the case of a rocket during its launch, the force generated by the rocket's engine is not the only force affecting the rocket's launch. Air resistance, friction and gravitational force are some the other forces affecting the rocket's motion.
Since the work-energy theorem only concerns with the work done by a net external force on the rocket, and not with any single force from the rocket's engine, the statement is false.
