I would say yes. You can adapt the process to your liking. I've considered doing that too but have other projects first. You don't really need their templates if you can cut squares accurately. Then you can make them any size.

There is a way that you do NOT have to do any hand sewing https://www.youtube.com/watch?v=-pL36s08wg4 that I an going to do.

I have done many types of QAYG and have never hand sewn anything.

This is the fun and done method. You make your backing 2" larger than your front block so you have 1" all the way around when the front and batting is centered on the backing. The batting is is the same size as the block front.
Quilt your block before you sew them together. To sew the blocks together put the right sides of the backs together and using a zipper foot stitch close to the batting and the front block. Once this is done you will have two 1" pieces of backing sticking up toward the front. Lay the block flat and take one of the backing flaps and fold it with the raw edge next to the stitching (in other words, fold it in 1/2") then fold it again over the front. You'll have a 1/2" sashing on the one side of the block. Stitch close to the folded edge. Do the same on the other side. The end result is that you will have a 1" total sashing of the backing fabric showing between your blocks. Continue this across the row. Joins the rows together in the same fashion. Once all the squares are joined you will have a 1" of backing fabric showing all around the edge of your quilt. Use this for the binding. Fold in 1/2" and then fold over again and stitch close to the folded edge. You can miter the corners or fold them them at 90 degrees to complete.

Here is a picture of sewing the rows together. In it you can see the sashing between the blocks and the zipper foot sewing the rows together. This was a baby blanket so I didn't use batting but used an extra layer of flannel instead. The squares were small (3") so I didn't quilt each square either. I was using up some tiny scraps to make this.

Those pictures explain it well. You would have to be careful when picking your front block pattern so that your sashing / binding doesn't interfere w/ the block design. It was perfect for your "whole cloth blocks". I bet it would be great w/ applique blocks too. I think it would need an extra step for most pieced blocks, I think if the pieced block fronts had a narrow border added before sandwiching that would take care of loosing points and patterns in the pieced block.

Oh and I meant to say what a great idea that is for a quick and easy baby blanket. A fabric w/ a print that could be fussy cut for the front squares and a coordinating back print.

Cotton Theory is similar to this, but with Cotton Theory, both top and back pieces are cut one inch larger. The batt is placed between them and that piece is then quilted. She did the quilting with decorative stitches on the sewing machine. All pieces are done this way. If a square has strips around it, the square and each strip are cut one inch larger, the batt piece is centered between the top and back; it is quilted and then added. The seams are made in a very special manner to make "high-ways, freeways, one way streets and sidewalks". And you have to be very careful about your "intersections". There quilts are always reversible. They look good from both sides.

I made one this way and was glad I did.