It won't hurt "performance", but it may block the signal depending on how thick the plastic is. I.e. if you have a lock on GPS, you're good; but if you don't get a lock, it's the plastic. The way I understand it, plastic isn't going to cause erroneous position readings because it isn't delaying the signal, but it can block it which means you have no position.
Is there any way you can mount the GPS puck on top of your plastic?