I've done it, but with a walking foot. I bought the book,
Divide and Conquer! Quilt It Your Way, by Nancy Smith and Lynda Milligan and the way you describe is one of the tutorials in the book.
They describe it this way:
First, Make the top in one piece. Then, sandwich the whole quilt, but spray baste or pin the center section only (1/3 usually). (I spray basted, so used newspaper to keep the spray off the parts I didn't want to stick.) Then you fold back 1/3 of the backing and top, leaving the batting only. Then, you cut the batting away. She suggests you use a wavy line. Then, repeat on the other side. Quilt the middle. Add the backing back on one side, using pins or spray to adhere it. She suggests a whip stitch to sew the batting back. Quilt that, then repeat on the other side.
I thought I was very careful to mark the batting I cut away to show exactly where to place it when I added it back. I could not get it to fit right, so next time, I'll just cut it straight. I tried to use that adhesive that you iron on to join the pieces. That didn't work, it just melted the scrim on the batting. I finally just zig-zaged it together. It all worked out. Maybe if I had just hand sewed like they suggested, it would have worked better.
Like I said, it worked out fine. There was a little bit of frustration, but that's how almost all new experiences are. I'd leave 2 1/2 to 3 inches free so adding the batting back will be hiccup free.
They also have a method for adding the borders after the center is quilted. It is a book worth having. Used, it's $5.19 on Amazon.
https://www.amazon.com/gp/offer-listing/1880972433/ref=sr_1_fkmrnull_1_olp?keywords=divide+and+conque r+quilt+it+your+way&qid=1558216649&s=gateway&sr=8-1-fkmrnull
bkay