There are likely to be some special touches at the UK pavilion in Epcot, and Pleasure Island is doing a special event on Mar 12, 13 & 17. They'll have special entertainment, live Celtic music, leprechauns, bead throws, and other festivities.
But beyond that, there aren't any special parades or anything.
I just found out I'm going, so am being a little silly right now. Nothing like an impromtu, unexpected, all expense paid trip the the World to make one a little silly!