We consider soliton-soliton interactions in the damped ac-driven nonlinear Schrodinger equation, which is the simplest model of charge-density wave conductor or of a cold plasma driven by an external ac electric field. Analyzing perturbatively the collision of two solitons with zero initial velocity at infinity, we demonstrate that after the collision the solitons separate at a finite velocity, i.e., a two-soliton breather does not exist in this model. We corroborate this analytical prediction by direct numerical simulations. We also demonstrate that soliton-soliton collisions in the model considered are practically always destructive: After collision, the solitons find themselves kicked out from the stable states, phase-locked to the ac drive, and finally they fully decay under the action of dissipation. Using the results obtained, we calculate a contribution of the solitons to the rate of absorption of energy of the ac field, which is the most important experimentally observable characteristic of the above-mentioned ac-driven systems.