I would not recommend putting plastic on the bottom rack of the dishwasher as the heating element in the dishwasher could potentially melt the plastic dishes.
I've had that happen to me before when I put the plastic dishes on the bottom rack they moved into the heating element or got close enough to the heating element and melted some of my plastic dishes.
So I would always just put the plastic dishes or any other plastic in the top rack of the dishwasher to keep the plastic away from the dishwasher heating element.
Otherwise you risk melting the plastic.