It depends on the preamp, of course there will be a drop off in performance, thats what an active system is there for. But some preamps are clean, meaning, they will not colour the sound either in active or passive, with (importantly) no drop in volume when switching from active to passive.
Some preamps are coloured specifically for there manufacturers tone. and also when you switch the battery off, you will get a drop in volume and the specific tone to that preamp.
What bass are you referring to.?
The experts will be along soon.