If the eyelet holes are small and the batting is bonded, it will work. I have incorporated eyelet fabric in several baby quilts that were successful and didn't poke out. Another idea would to use Polar fleece instead of a batting. That certainly wouldn't poke out and likely would be even warmer than most battings. I love your idea of adding a ruffle around the edges and then "birthing" the quilt. It will be a lovely, very appreciated gift! Please publish a picture when it is finished.