I've embroidered on clear plastic, so I don't know why not. I didn't change my needle (75/11 Organ needle). Just try to find a design that isn't so stitch intensive.

I have embroidered on vinyl tablecloth with a cloth backing and didn't use stabiliser. I used double sided tape on the edges of my hoop an stuck the tablecloth to it instead of hooping

Someone did some beautiful coasters on vinyl tablecloth just recently. There were photo's up in projects. I am going to give it a try when I find a white plain one.

No harm in trying. A couple of trial runs first. Please post in projects when you are finished - would love to see the result

I also have done this before & have had no issues with it I did use warm & natural batting under it to make it as soft as I could for a baby & Carolyn has shown us how to use it for the backings for coasters. She has done them with great success. I agree with Jrob not to use to dense a design~hugs~

I use the cloth backed vynal on coasters all the time in coasters. I usually put a layer of cotton bat in the middle. I'd suggest that you put the design in a corner as an extra precaution against leaks as the needled does punch holes in the vynal. Don't use too dense of a design.

Joann Fabrics has a fabric called PUL (the letters may be mixed up) that is good for changing pads. I made a sandwich with it and flannel. One I finished like a pillow, the other I used a binding. That way you can do any design you want on the fabric side before sewing together. They also had some with designs on it. It is usually found with the craft supplies instead of the fabric.