I'd buy that the impulse engines (always described as conventional rockets in the 1960's and 1970's tie-in material, by the way, and very strongly suggested as such in TOS) are fully effective only when a low-level warp field is also used, but not
that the impulse engines themselves
reduce the ship's mass.
Another reasonable alternative would be that inertial dampeners are required for high impulse acceleration. Or, I could by that inertial dampeners are implemented via a low-level warp field.
However, the very term "impulse engine" implies propulsion via Newton's third law. Hence, the original conception of them as nothing but rockets, possibly using nuclear fusion as the reaction.