Will I lose image quality by adjusting white balance in post processing?

No. If you shoot in RAW, there is nothing lost.

In fact, in RAW, the white balance you set in-camera is nothing but advisory information to the post-processing software. A different multiplier is applied differently to the red, green, and blue channels during RAW conversion depending on the setting, and if you're doing that conversion from a RAW file, you can always choose to do it differently unless you destroy the original.

The only exception is when the lighting is so strongly colored that it affects the metering oddly. If you have the white balance set in camera, it will apply to the displayed histogram. Some people really are concerned out about this, and have invented the idea of "uniwb", a custom white balance designed to balance the three color channels evenly. If you are very meticulous, and if you are trying to make the most of extreme scenes, you may be interested in seeing if that helps. (You probably also want to reduce the default contrast settings, for the same reason.)

Also, see this related question: If shooting RAW, is the white balance selected in camera irrelevant for exposure? I did a simple test, and my conclusion is that even in an extreme situation, the metering isn't thrown off by more than a third of a stop. This is likely to also be the case with the histogram, and therefore, I would recommend not really stressing out about uniwb.

If you shoot in JPEG only, the application of the white balance multipliers is destructive, and difficult to compensate for if you change your mind. But I don't think that's what you're asking.