I have also used straw bales on plastic and grown everything. My soil was contaminated by weedkiller so I wanted to ensure no contact. Potatoes, beans, courgettes all grew well. Needs a lot of water and fertiliser.
Is the plastic the type that drains, how will you get it out again if covered in soil.
But a great idea, I am suffering from stinging nettles. So will get some bales.