Long Distance Competition/Ultracycling, Randonneuring and Endurance Cycling - Century on a Time Trial Bike?

Have any of you done a century, or any long distance riding on a time trial bike in full time trial gear? I'm curious because this sounds really fun, but probably tremendously painful on your poor back, and might look goofy biking that far with an aero helmet on.

Me personally? No, but the Brits regularly do long distance TTs. Up to 12 hours, an aero bike is standard. They are fairly quick though, the top riders are close to 3.5 hours for 100 miles.
http://www.cyclingtimetrials.org.uk/Home/tabid/36/itemid/1427/Default.aspx

Never personally done it but know plenty who have. Trick is to get done with the ride before it gets too uncomfortable. If you're shooting at 4 hours or less it's the only way to fly; comfort isn't high on the priority list if you're riding for that kind of time.

under 4 hrs?!... and i thought i was doing good if i hit below 5

I've done a lot of long distance stuff on a TT bike, Team RAAM, FC508, Hoo Doo...yeah, with an aero helmet! ;) It's not as comfortable as the regular roadbike but if you are fitted properly it isn't bad. TT bikes, if they are fitted properly, are fitted for speed and efficiency with comfort coming in last. For longer distances you need to compromise your fit a little bit so that you can do the distance. For me the back isn't the issue it's the seat! On the TT bike it is difficult to find a comfy seat position without causing numbness issues. That will take the most time and effort to get right.

Just finished a 50 mile ITT on Saturday on my triathlon bike but I don't have a skin suit or aero helmet (but I did wear a very snug fitting lycra jersey). I had no back, neck or shoulder problems riding aero the entire time. I did have some seat issues because I was pushing hard and I tend to get up on the nose of the saddle more when I do that. I am going to attempt a 12-hour on this bike in 5 weeks and perhaps a 24-hour later in September (I'll see how the 12-hour goes). I will likely sit back a little further on the saddle for the longer stuff (like I do in training rides) so I don't expect any seat issues in these.

I saw a few TT rigs on the 160-mile Ramrod mountain ride recently.

The fastest do that ride in about 8-9 hours (I think), so they were definitely spending lots of time on that setup, which is pretty impressive.