I have done binding by machine numerous times. I usually stitch it on the back and turn it to the front. My key to success is to press it very carefully after the first stitching being sure to press toward the binding. Then, when I turn it to the front all goes well and looks straight-especially it you use thread to match. I cannot help but think you could follow the same procedure if doing it after you stitched to the front first. I would recommend not using invisible thread because of danger to little fingers if the ends pull out. I would use a simple decorative stitch on the front 'just in case'. Good luck.