I've been reading up a little on crossovers in regards to crossover points and the marriage (if you will) of components.
You have 2 types of what I'll call external crossovers, passive (after the amp) and active (before the amp).

If you're controlling these audio components through the DSP, are external crossovers still needed?

 

I would say no
That would be a Active crossover
The Passive crossover should be what you replace . (External)

And to clarify Passive means its a physical device with coils and filters, it can go anywhere inline, and requires no power
Active is a device that requires power.
I would say THE DSP would replace both types
But depends on the capability's of the DSP