"Although CAS, TAS and Altitude are measured by barometric means and computed for display on electrical ASI/Machmeters and Altimeters by the DADC, Vertical Speed is usually inertially derived and presented on an electrically driven IVSI."
Veering off topic here, but....
Aircraft with IRS's usually need ADC info for the IVSI. In fact, the IVSI won't work without it on 767's, 747-400's, etc... (try pulling the relevant ADC breaker and see what happens to your IVSI). The IVS is a combination of both inertial and barometric info. The baro provides long term correction. In many cases, the air data is not fed directly to the indicator, but via the IRU (so it may not be immediately evident that the air data is being provided to this instrument).
Back on course...
IRS's compute position relative to the ground (if the aircraft drifts due to crosswind, the IRS's still know where the aircraft is relative to the ground). It's only when a display of windspeed/wind angle/etc is required in the cockpit that conventional air data is required.
Regards.
Q.