I've used my PBC "in the rain" several times but not actually "out in the rain" if that's what you mean. Using it uncovered in any way won't hurt it, I'm fairly sure but there's bound to be some cooling effect -- how much I don't know. Also, lighting charcoal in the rain might present some challenges. The dished lid is going to collect some water and probably will steam as it heats and evaporates.
Know anyone who has a pop-up you might borrow? That'd be my recommendation for staying at least partially dry. You could also cook just inside the open door of a garage or maybe on a small covered porch? At the very least round up a big golf umbrella and an "assistant" to hold it over you as you toil away in the interest of better groceries.
Half the fun of being a dedicated outdoor cook is cooking when the weather isn't nice. Rain, snow, sleet, hail, locusts, pestilence, whatever, food just tastes better cooked outdoors. Do it. The PBC won't melt even if you do
Hub