No, you're putting force on a two dimensional area -- it's more than one thread wide. The stay stitching provides reinforcement for two threads, one on either side of the thread. What you're dealing with is mechanical stretch -- the bias is stretchy because the fabric is mechanically distorted. One, or even a few, lines of thread aren't going to stop that. (I tried this, even though I didn't think it would work, on a shopping bag that was meant to fold up super small. The bottom sagged alarmingly, so I thought some stay stiches would be easy. didn't work, but a piece of cotton twill tape inserted into the corner seams, run across the bottom to the diagonally opposite corner, help a lot. Until the handle ripped out, at least.)
I suggested tape because it's a standard solution for stays like this, you're likely to already have something suitable, and there's probably a way to also make it a functional attachment. I think I'd actually prefer a reinforcement of the fabric by layering two plies of the bag's fabric. Or maybe figuring out how to change the design so there isn't a load like this, or changing how the panel is cut so that forces are put along the grain or crossgrain. That might not be possible, because it creates other problems.