Can't find anything on this.   Live piano-playing produces a slight "randomness" in chords and in any two notes hit simultaneously.  Notes are never hit exactly at the same time, as in a perfectly quantized midi file.  Instead, real playing produces notes that are slightly off the beat and slightly off each other. 
 
Can't find anything in Cake that makes that "random" effect.   Does it exist?
 
 

There are several CAL scripts. HUMANIZE.CAL, RANDTIME.CAL and "Random Time.CAL" are three that I found that vary MIDI data. There could be more, I did not spend much time looking.

When I record any keyboards I record both the audio and the MIDI. This gives lots of options later. I'm taking about recording real talented players here, not me, I suck. 
So I have spent many hours editing or just looking at "real" piano ( keyboard)  data in the editor. 
Your assumption that real piano ( keyboard) notes happen out of time and off the beat is not actually correct. The notes are perfectly (one would hope) or very, very close to where the player wanted them and with multiple variation of "time" which involve more than I can explain. Lets just call it "feel".  And each style of music will involve a different "feel." Understanding music and what the original piece should  "feel" like helps immensely when editing and especially using any quatizing. Example quantize a Bluesy swing piece to 16th notes will kill the swing. You probably will use 16th triplets to get a better "feel". 
 
I think what your finding is possibly entering notes manually results in a very stiff, mechanical sounding part, correct? 
Entering notes manually and getting good results actually takes better computing/ editing/ and most importantly an understanding of music than playing it poorly on a keyboard and fixing the mistakes. 
A computer can only take a perfect piece of data and make it sloppy. Is that what you really want?   
There's more to the notes than just the timing offsets, there's the velocity too. 
Most of the time when "looking" at what was played by a real good player I'll see a huge variation in the velocity of each chord, as well as "aftertouch" and the "Sustain Pedal" are involved. You'll see a lot of false triggers too, Adjacent notes that are accidentally played but at such a low velocity you can't really hear them.  
 
So I would play with adding the dynamics before I would go messing with putting notes in possibly the wrong place. It's a huge job really if you try and do this. It's much easier to just try and get as close as you can playing it yourself and then editing in a way that does not remove the "feel" 

Just to put the question into perspective.  I've been playing classical for 55 years (since I was 5) and can get through most of the really difficult technical rep (eg Rach 3, Beethoven pc 4, Bach's WTC, Brahms pc 1 and 2, etc., etc...) 
 
Midi has been a fun thing for me since the early days of Atari, and before that, crude programming on BASIC (we're talking 20 years ago).   I get super-interesting feedback on my own playing using midi technology.  Also, I think any pianist who is honest has to admit that with the most recent piano samples (not so much the earlier attempts), a solo piano recording can be (at least in some cases) virtually indistinguishable from a live recording at the "real thing" (which I do as well).  
 
My question re note positioning really comes from a very narrow concern: I've been taking a closer look at the "midi-trail," so to speak, of my own playing, particularly in respect to the faster preludes and fugues from Bach's WTC (Well-tempered Clavier).  All I'm trying to do, here, is to compare the non-random note timing discrepancy that occurs in playing, say, the second prelude from Bk 1 of the WTC with a "fake" or "midi-generated" discrepancy.   I have the CALS mentioned above, and mea culpa for not experimenting with these first.  I thought, possibly, that there might be a series of quantize parameters that put together might randomly nudge the notes in a chord (or any simultaneous played notes) a few ticks away from each other.  
 
Actual piano playing does this, of course.  But in a non-random way, as folks point out above.  If you examine the midi file of any live piano-playing, you'll often see that the leading or most important note of any chord, or any 2 or more notes sounded together, is a few ticks (let's say milliseconds for the sake of argument) ahead of the less important notes.   Also, it's velocity will be pronounced relative to the other notes in the chord, obviously. 
 
Seems to me that it would be interesting to see how much of this aspect of human playing can be midi-sculpted into an otherwise artificial midi file.
 
That's a tiny bit of where I'm headed here.

I normally put the loudest note exactly on the beat with the others slightly late and maybe one note early.  This seems to sound best to me.
 

Which is pretty close to what we naturally do at the piano.  Just ran the humanize cal, which used in tiny, tiny amounts is not bad.  But it doesn't do what you've described.  I suppose a seasoned programmer could create a CAL for that.  Used to make up CALS, but I'd have to "re-learn" the process!!!

If you're capturing a midi performance over a genuine midi cable, keep in mind that the fastest rate of transmitting notes is between 2/3 and 1 ms per note (depending on whether running status is used or not). In some cases, when notes are ending at the same time other notes are beginning, the rate can be even slower.