A lot depends on the tightness of the weave of the fabric and if it has borders or not. I am currently handquilting a quilt whose top was made of loosely woven feed sacks. A lady at the Senior center donated it to benefit the center. It had no borders. I took it home and stay stitched he whole outside before washing it to be sure it would not fall apart. I then pressed it and added a solid border on all four sides. I currently have it more than three quarter of the way handquilted and it is doing fine.
Staystitching is a good idea if there are no solid borders or if the blocks have a lot of bias edges. It is mostly a judgement call.