Yes you can, just make blocks and use the quilt as you go technique to put the blocks together.
https://www.google.com/webhp?sourceid=chrome-instant&rlz=1C1ASUC_enUS565US565&ion=1&espv=2&ie=UTF-8#q=quilt%20as%20you%20go%20technique

If she has embroidery machine (or access to yours), it's worth the money to buy the Anita Goodesign "Mix and Match Crazy Quilts" set. All in the hoop. Saves time, fabric and fingers. Gotta love it. When you're through on the machine you're almost through! Attach the back ans stitch in the ditch.

yes its possible do it useing paper piecing but the embroidery machine can do it to but i found it took far longer that way.

Husquvarna/Viking also has some that can be purchased: Patchwork Quilting #238 and Patchwork blocks #147. Lots of designs in each set. There are others also available. Rather expensive however. Also try Embroidery Library.

Hi Carolyn - I haven't done a full quilt but also prefer stitch and flip to appliqué crazy quilt machine embroidery. I would do blocks, then stitch them together as in this video, although the grid would have to be ok with your granddaughter (there are other methods for joining blocks on YouTube). For TWELVE BOM stitch and flip quilt blocks for FREE (she's taking them down at the end of the month - ONLY sends a newsletter with links to the designs on Mondays, so you'd have to sign up now and wait until Monday for her set of 12; set to individual email as the newsletter comes as email - she gave up on Yahoo groups as so many folks had issues and only uses it to keep her newsletter email list, she does not spam or send lots of mail). Anita Goodesign uses appliqué for most of their crazy quilt blocks (as does MollyMine). I was VERY disappointed with the HV set - for the price I'd expected to at least have different color stops in the top stitching. It was so much less than blocks I was finding for free. I'll stop here and go dig - I have other stitch and flip designs but need to go into my files.

Posted the Anita Goodesign appliqué free crazy quilt block set as tagged "freebies" on this site.