No,
FMCs get there info from ADC, GPS, IRS and database which, while related to flight teat data, is modified for the particular airframe. ADCs NEVER recieve wind information.
How much? Well, which aircraft under what circumstances?
A slow flying aircraft in a wind that represents a high percentage of it's still air Vx? potentially a lot.
fact remains the question was "Does it", and the answer is "yes"!