Most plastics are designed to transmit light through the flat part of the glass, and not transmit the direction you are thinking. If it worked that way, there would be a lot of loss to the glass/plastic and it would appear opaque, more or less. There is a special type of plastic that absorbs light on the main plane and exits it along the edges. You see this stuff made into all kinds of whirlygigs in nick-nack stores. Chances are, whatever light is emitted inside the plastic will just exit through the main plane and not much, if any would be transmitted to the edges.
My ex-wife and I used to have a tradeshow display business and I did a fair amount of experimentation trying to come up with some cool stuff, and I was never able to get a good lighted edge to a piece of plastic, and I tried many different types and techniques.
However, having said all that, it would be cool to hear what you get for results if you do try it!!