A simple answer to your question is "Yes"
Every crossover point causes a phase shift. No matter active or passive.
In your case, the active crossover will kick in first and when the signal will reach the inline capacitor, it will be 6 db down at 3 Khz. The passive cap will start to filter at 3Khz with the rate of 18 dbs per octave. So combination of these two filters will have a cascading effect on signal in terms of attenuation.
Now a passive or active crossover point shifts the phase symmetrically measured in degrees. While cascading filters will shift the phase all over the plot and it will be a nightmare to get everything in phase throughout the passband.
If we were to measure the impulse response of tweeter whilst the 2 filters are in place, the phase shift can be measured in degrees but the problem is that we don't know what the environment is doing to to phase and how the tweeter is interacting to other drivers in system. Less phase issues = More cohesive system.
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