I have made many embroidered pieces into quilts and wallhangings. I have finished them in several ways. From my experience, if you put batting and quilt the border, the embroidered center tends to puff a little and sometimes a lot. The only way I have prevented this is by stretching the whole thing on stretcher bars to hang it up or to frame it with no glass. When I defiitely want to hang it as a quilt without a frame, I them quilt over the embroidered with invisible nylon thread and use a very light quilting pattern like large stipples or something like that.
Please take a look on my web site to see a few finished pieces.
http://maria-quilted-treasures.com/index.html
Maria