You can always try. At the last quilt show here there was a rag quilt shaped like a turtle. It was really nice. If nothing else, there isn't anything that says you couldn't have a couple blocks that weren't rag squares or you could make the star and the fabric surrounding it would be rag. So the star it self wouldn' be ragged but the block it was in would be. I hope that makes since.

I did a double Irish chain then rag quilted it. On some of the blocks, I simply straight-lined quilted while on the alternate blocks, I did a fancy quilting pattern to hold the blocks together. I put the raggy edge on the "back" which was flannel so when face-up, you don't know it's raggy and it looks like a regular Irish chain. And, vice versa. My DD tends to prefer the flannel side up and since it's on her bed, it's her choice.

I would tend to make the Ohio Star on just the top fabric of the square/diamond/ or whatever background shape you want. I would sew it as an applique but not let some of the edge of the star piece overhang so that the edges could be ragged. That way the ragged edges wouldn't be so large as to overwhelm the Ohio Star;

ali