I've had the 3800 for a few days, and so far I don't see any appreciable usage from cleaning. Someone else had said that head cleaning usage would be reported on the next print in the jobs view.
Prior to making my first print, I did one manual head cleaning, and about three automatic head cleaning/nozzlecheck cycles. Somewhere in there I did a head alignment. All the log shows is the head alignment, followed by my first print, which was an antelope canyon print (this becomes important soon).
The clogged nozzle appeared to be a magenta nozzle. The first print shows the magenta usage at .43ml, which is pretty high for an 8x11 of antelope canyon, I think. Hopefully that is the case, and the printer is smart about which nozzles it pushes ink through on an auto nozzle check head clean cycle. Otherwise, it didn't keep track of how much ink was used. I think I'm probably being too optimistic about this. I hope not.
Initially charging the printer seems to knock the cartridges down about 20%. I'm not sure I saw any significant change as a result of the cleaning cycles, but it's hard to say for sure.
If you look at the inkjetart site at the 3800 page, I'm not sure where on the page, but there's a job output from their initial usage. In their log, there are some extremely large unexplained (at least I couldn't figure out what they were from) ink usages in a single 17x22 print. Seemed much larger than some other 17x22 prints.
This was probably more than you wanted to know, but without specific numbers provided by Epson or the printer, I think we're all guessing right now.
At any rate, I'm having lots of fun. I think so far it is a great printer (compared to my 1200 at least).