No, you do not... Unless you did something wrong of course ;)
The importance is to calibrate your monitor to sRGB color space. Once it is setup that way, then giving it a known input will result in a known color. My setup is OpenSUSE with Parallels Desktop and only the monitor needed to be calibrated.
Some people calibrate their graphics cards instead of the monitor which can give banding issues but should affect both your system and the virtual machine, unless the VM's machine bypasses the cards calibration. In this case I would not know if it works with your setup or not.
Some applications can be calibrated themselves which makes them change the colors they send to the monitor in order to get the desired color. If you did that, then only that application would produce the right colors.