You question isn't very clear. What type of crossover? And into what else?
Active crossovers feed Amps.
Passive crossovers feed speakers.
How is the crossover damaged?
As to a 'driver' going into something else, for the most part, a 'driver' can only go into a room.
I'm sure you have a legitimate question, and many here are willing to help, but I think you need to explain what you are talking about in a little more detail.
I think in general, the answer has to be YES, it is possible for a damaged component to alter what you hear.