I've done it a few times on long walks, although its debatable how 'public' it was. I chose times and routes where there would certainly be no crowds, and might only cross paths with one or two people over 4-5 miles. Staying downwind as we passed, its unlikely they smelled anything at all.
Then there was this one time.... Went to Junior's to watch a Blackhawks playoff game. Walk, rather than drive, as adult beverages were involved. On the way home, 1am, 1/2 mile from home, I really, really had to pee. I thought, why not? No diaper, but the neighborhood is completely dead, Mrs. Maxx is out of town, just let 'er rip. Much to my surprise, when I relaxed the pee muscles, a horrendous mess exploded from the other end as well. I don't think I left anything other than wet marks on the sidewalk, but the cleanup is not something I'd care to relive. Ever.