The main advantage of active ride in F1 would be that you could decouple, to a degree, loads coming from aero, load transfer and road irregularities and deal with each of them seperately. You can then setup something which is very "stiff" against downforce and load transfer in order to keep the car at the optimum ride height while cornering, braking and accelerating but soft over road irregularities. This gives you a double edged performance gain in aero and mechanical grip.
This decomposition of the tyre loads is not practically possible with a passive system. Then add to that the fact that in a passive system each part can only move in the direction that an external force is pointing. I.e. having the car lift itself up as downforce increases is not possible.
Other ways it can improve performance is by running very low ride heights to lower the CG without worrying about hitting the ground in pitch and roll. Another trick could be to lift the body to a low drag attitude under acceleration to improve top speed.
I'd say seconds of laptime improvement is realistic. Though such a system would be definately be seen as a breach of the moveable aero rule. So either the rule will change or the active ride controllers will be extremely limited.
Dave, based on a few job postings I've seen around, your company seems to be gearing up for some active ride work