Nope, the standard two way system in the car does not have a crossover, only the uprated 3 way system in the 10 speaker sound system.
If you put uprated 3 ways in, they come with their own crossover, so you would then connect the 'harnesses' that come with the speaker adapters to the original harness and plug that into the crossover.
The harness is quite different for the factory 3 way front door speakers as is the plug that goes into the factory crossover.