Yes, I have been doing full size pieces for chair seats. I have wood on my property that is suitable for this. Quartersawn works best, but if you can imagine, that takes a a trunk that is about 3' wide, min. A green quarter sawn piece I have been working on still cupped on me, but I clamped it flat again and it seems to be complying. You can also get a chair seat out of a 18-24" or so, log which is flat saw, staying out of the pith, but must be dried in a stack, to keep it flat, and then you don't have the really nice benefit of saddling a seat in green wood. Great thing for chair parts, is I can start with a 22" round, and split out parts, including chair seats on a splitter, then stack em in a pile. Smaller chair seats, which can actually be quite comfortable, can be as small as about 14" or so by 16" or so. I also think, with rounds, that a book matched chair seat looks really good, so you could make an 18" wide chair seat out of a 20" or so round. All of this, obviously, can be influenced by species. On chairs, I work almost exclusively in West Coast Tanoak, which seems to be a lot like Red Oak, which we have a lot of around here, and has been severely impacted by sudden oak death, Ambrosia Beetle, and fire. So, for the time being any way, there is a lot of available.
So, for usability of chair seat cut out of a round from the dump...I think you may do well. I would definitely seal the ends as soon as you cut it. If you get some nice rounds, buck em into 22" or so, then split them out in front of the shop. Watch out for imbedded metal-might be one of the biggest hazards in mining dump wood.
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