The advantage of ticking Don't affect colors (adaption only) is that the Gamma 2.2 will not be burnt in to the final image, however V-Ray will proceed with all its calculations as though color mapping is applied. In effect this enables V-Ray to calculate better noise samples as it is sampling a brighter image, so the differences between light and dark tones are easier to detect.
The image you save out is still linear, so we still have the flexibility of compositing in linear space.
The V-Ray Frame Buffer also ignores the 3ds Max Gamma settings, so the render may come out looking very dark. You will need to click the sRGB button at the bottom, which is V-Ray's own Gamma correction. Note that this is only for displaying purposes; the image is still linear. As you can see, Fig.05 – 06 is now displaying a linear image corrected to be viewed at Gamma 2.2.
You will notice that from now on light will fill every corner of the image without the need to add a load more lights or boost any settings to unnatural levels. You will also notice that the image will not burn out nearly as much as before. This is basically because when you want to brighten the dark areas by adding more lights, this still contributes to the light areas, so you will inevitably end up with ranges that exceed pure white (255, 255, 255).
File Formats and Rendering
Compositing in 32-bit has been used in feature films for years. Color correction is much more flexible, especially when controlling highlights. The ideal solution is to export a linear image like EXR or DPX for example. With linear images all of the pixel data is mathematically correct as opposed to looking correct, resulting in accurate and predictable results when adding or multiplying in post. After Effects and Nuke can be setup to view linear images in sRGB colorspace, composited in 32-bit and then exported at 8-bit for broadcast.
When saving linear images, 8-bit formats will most likely result in some color banding. There often isn't enough range in 8-bit colourspace to represent a complete tonal range when working with linear images. So whenever possible always render out to either 16-bit (TIFs or SGIs) or 32-bit (EXRs, DPX).
Never use JPEGs for rendering as JPEG compression is optimized for nonlinear images and will throw away much of the data required for Gamma translations to and from linear space.
Burning the Gamma in
Burning the Gamma in will limit what you do in post, but if you want to then simply un-tick Don't affect colors (adaption only) in V-Ray's Color Mapping dropdown menu (Fig.07).

Fig. 07
You can tell this has worked because you can view the same image, but without having to click the sRGB button in the V-Ray Frame Buffer. You will notice that if you click the sRGB button it will preview Gamma correction on top of that, resulting in a washed out image (Fig.08). You get a similar result if you duplicate the image to the Max Frame Buffer. This is because we set Max to Gamma 2.2.
The Magic Linear Workflow Button
This button is a little misleading. It looks like if you tick it, then you will magically get proper linear workflow… but no, you don't. This button is basically a quick and brutal way of correcting the V-Ray materials that were not setup and tuned with linear workflow in mind. I wouldn't use this (Fig.09).

Fig. 09
And that's pretty much it really!