I don't know of one, but it is an interesting idea.
Areas with a lot of golf courses frequently have websites where you can go and make last minute tee times at a significant discount at courses that are not sold out. You can also go to travel websites and get last minute flight and hotel packages to places like Cozumel or Belize. It would be interesting to have a clearinghouse for such openings on dive boats.
The first time I did a liveaboard was about 15 years ago, on the Great Barrier Reef. We booked the trip about a year in advance, paying top dollar for the premier room. Our enjoyment of the trip lessened a little as we talked with the other guests, and realized that about half of them had had no plans to be on a liveaboard until a few days before the trip. They had been accosted on the street with an offer they could not refuse. My next few liveaboards were in very remote places, and I was part of a large group, so that was not the case. My last one--again in Australia--once again featured people dragged in off the street. I have to assume those people were paying a heck of a lot less than we were.
I think it would have to be in a place like Australia, where there are people who just happen to be there who might be able to go off for a week of diving at the last minute. If we are talking about Chuuk or the Galapagos, where you have to plan plane fares well ahead of time, it might not work so well.