With a recent version of Capture One you can output TIFF files with embedded camera ICC profile and also get the TIFFTAG_TRANSFERFUNCTION set. If you reverse that transfer function you should get back to linear camera data, pre-processed with white balance but otherwise in native camera color space. If it's a Leaf ICC profile it has also been preprocessed from camera RGB to Prophoto RGB though, using the CaptProf_color_matrix embedded in the raw file.
Note that a "linear" curve will not look linear, as it must also take into account the ICC gamma, which generally is 1.8. For an Aptus-II the resulting transfer function from a linear curve is almost exactly an x^1.8 function, ie effectively linear as the embedded ICC profile has gamma 1.8. For many other cameras (almost all?) there's deviation though, typically the transfer function leaves some space in the highlights. This might be due to give the ICC cLUTs proper headroom or to hide a noisy clip level which some cameras have.
My current understanding is that the bundled ICCs are generally designed for the "standard curve" or curves similar to it - probably all curves *except* the linear curve is "similar enough" to the standard curve. A linear curve is however far from this standard curve and therefore may cause the LUT conversions become a bit distorted, and thus it would not be recommended to use the bundled ICCs when linear curve. I've tried to find some "official" statement regarding this but not received any though. I guess they want you to take a course
I have not tested that many images but with a Leaf back and a Canon 5D mark 2 one can see that (white) skin get a slight greenish cast if the ICC is applied to a linear curve while it looks good with the standard curve. Depending on subject it may be difficult to decide which one is better, but if you layer the two images on top and switch fast between them one can clearly see that the color does change despite that you're using the same ICC profile, and with this fact I think it's reasonable to assume that the bundled ICC profiles have been designed to look good with the standard curve.