Yes, however there will be a little bit of damage to the fibers of the fabric. I will rip for my backings but then use a 5/8" wide seam to cover the damage area.
I suppose you could rip a little bit wider then trim off the damaged part. With a 1/4" seam, you may not want to rip and just sew.
I do rip off smaller pieces off of yardage to cut for projects. For instance if I have a 10 yard piece of fabric and I need only a 1/4 yard piece to use, I will frequently rip off just over what I need and then press and cut my pieces, but at least 1/4 to 1/2 inch away from the ripped side.
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My newest Grandson, Caleb Austin, was born May 29th. I am now Grandma to 4 precious babies. I am so blessed!!!!