No Alistair, they won't find a food source, these are pet birds that eat out of a dish.
They have no idea what plants are safe or unsafe. What berries are available, nor where to find them.
Most escaped parrots starve, or are eaten by predators animals.
Very few survive, a few that may join another flock, will have a chance in a temperate climate.
And most birds have no idea of the surrounding area. How would they find a way back?
I'm not saying it can't happen, in fact I'm pretty sure most escaped birds want to return home to safety and food, it just doesn't happen.