I'd be interested to know if the parks in general do anything different on that day? Food, merchandise, even little things? That'll be our last day there.
Usually, the restaurants in DTD offer special menu items for St. Patrick's Day (some only on that day, others for longer), but those often aren't announced until a week or so beforehand. There is probably a small amount of merchandise (e.g., a limited edition pin, a plush, an antenna topper, etc.).