I think not – since you bring back (and resaturate the colours) anyway.
When you partially desaturate them, you introduce ‘crosstalk’ between the channels.
Suppose you start with something like
R: 0.8, G: 0.4, G: 0.1
Desaturation means R decreases, G increases slightly, G increases more (you get closer to grey, where R = G = B). This means, when applying the curve per-channel, the curve will have a more similar effect on all channels. Remember that an S curve tends to reduce small values and increase large values (but increasing already high values by just a bit, mid values quite a lot), increasing colour differences and shifting colours towards those secondaries (the ‘middle’ component starts catching up with the highest). This pushes most colours towards the secondary / complementary colours (orange, magenta, cyan), with sharp primary dividers between them. I’ve started to write an article about this, but currently can only give you these charts – I hope I got my conclusions right:
The ‘N6’ (Notorious 6) look like this:
By messing with the primaries:
Read a lot about this (I did not read the page in its entirety):