Well, I dug deep in the internets and all I came up with is this:
I don't know that there is necessarily a predictable relationship between the two as individual response to a change in either
varies significantly. If you move your cleats back 10mm, then *generally* seat height would drop somewhat because you are reducing ankle movement somewhat as well as extending the leg more. I underlined 'generally' because I've seen exceptions where a more rearward cleat position caused a change to the rider's pedalling technique to the extent that seat height could be left unchanged or on rare occasions raised.
If you moved your cleats back 16mm, you will almost certainly have needed to drop your seat height. Possibly up to 10mm.
But I did come up with this regarding saddle fore-aft/height (probably the bit Tinea was talking about). Comes in pretty handy because I'm putting the saddle a bit more backwards to.
With most seats, moving the seat forward decreases measurable seat height and moving the seat backward increases measurable seat height. Typically, if you move a seat forward 3mm you have reduced seat height by 1mm and if you move a seat backward by 3mm you have increased seat height by 1mm.
Slightly off-topic, but I always seem to forget how much valuable information Steve Hoggs website has..
For example, instructions on changing seats at the bottom of the post: http://www.stevehoggbikefitting.com/blog/2011/09/all-about-smps/
Figured this out by myself already but he explains it very well.