Hi, first post here. Pick my new (to me) V70 up in a week
If the kit you refer to is anything like the MK6000 (I've fitted 2) essentially the answer to your question is very likely no.
The Parrot kits come with a blue box that taps into your headunit speaker wiring. When you feed the parrot a music source the blue box essentially disconnects the headunit from the speakers and feeds them an amplified source.
So, when listening to music via the Parrot you are using the blue box as an amp, your headunit is completely bypassed. Volume control is via the control knob on the parrot. It doesn't sound bad by any means but will be no match for the fantastic Volvo head unit.