I would not sew through those... If you want to quilt through the image I would suggest buying the printer sheets that you print the image on..then you can quilt anywhere on them.
These transfers are not as permanently embedded into the fabric and they also tend to start peeling off after a few washings as well as where they are folded or rubbed.
Just my experience with them...my kids use these for tshirts...but they don't last very long.