It would be very slippery and satin frays like crazy. Ironing it to a fusible would provide body (people who make quilts from silk ties often do this) and prevent fraying, but does add stiffness and weight. I would experiment with fusible tricot to see if you like the result.
Another experiment you could try is heavily starching the satin before cutting. Mix a 1:1 solution of Sta-Flo laundry starch and water, paint it on the satin, throw the saturated satin in the dryer, then iron with steam. The starch would rinse out when the quilt is completed, leaving the fabric very soft. If you experiment with this and like the result, I would definitely recommend using 1/2-inch seams rather than the usual 1/4-inch seams because the satin will still be prone to fraying.
I would get a yard or two of satin and try both methods before committing to an entire quilt made out of satin.
I worked with satin years ago when I sewed a Halloween costume for my young daughter. I pre-washed the satin and the dress was able to go through the washer and dryer just fine. It was slippery fabric to work with, though. That's why you probably need to either fuse it or starch it heavily in order to get accuracy when piecing.