A very complex issue. Much will depend on the stitch count and design.
A high stitch count will most likely pucker and pull. Additionally if the design has fill stitching you can almost bet on cupping and fabric distortion.
Even the thread used let alone the backing will come into play. Example rayon thread will react different than poly thread. Hooping comes into play also.
Seeing the logo would help however the dead give away is the product mentions a heat transfer branding instead of embroidery.
I no longer embroider but if I did I would not stitch this garment. It could work but it will take a bunch of finesse not fitness
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mooseman