The invisible thread I have used for machine applique is YLI's nylon monofilament .003. This thread would never be used for satin stitching, though. Usually satin stitching is done with cotton or polyester thread. Although I have a spool of polyester invisible thread, I cannot imagine using it for satin stitching either. The stitching would become very hard.
At the very least, try whatever invisible thread it is that you have on a sample piece first to make sure you will like it.