Yes, the plastic will present a problem. As well as restricting growth, the soil won't get any moisture or air underneath the plastic. If you want to keep the plastic under the rock, your best option for plants is containers set on top of the rocks. There are nice annual grasses you could plant in them that would serve this purpose well and in the right container (maybe some made of hypertufa?) would look nice. Downside is, you'd have to plant those containers every year. Upside - your bed remains weed free.

There are grasses that do well in containers, provided their pots are big enough and have excellent drainage. Below is a link to a good site with lots of information. (Scroll midway down the page for tips on growing in containers.) FYI, cool-season grasses break dormancy and green up earlier.

Here is a link that might be useful: Limerock-grasses in containers