This curve is optimized for the default, linear, matrix profiles, so if you use an input profile like the one from C1, with its own embedded curve (which has a small dip in the lowest part), the contrast is likely to be too much.
You could design your own curve following the ideas in this post, or you could use the LUT module. Or you could do it by hand, using the darktable’s color picker and making a set of sample points from a photo of a colorchecker chart (e.g. the IT8 chart used by DPReview in their studio scene comparisons) – note the mean L values of the 24 White to Black wedges in the Lab readout and compare with the file rendered by C1. Then modify the base curve accordingly (it’s better to switch the curve view to logarithmic scale in order to have greater control over shadows). Save it as a preset, and the whole could be made into a style which you can apply automatically on import, etc.
I don’t know if that’s possible. Anders Torger (the author of DCamprof/Lumariver) reverse-engineered the C1 curves but I think they are camera-specific.