I don't think it's likely an experiment like this could last longer than a year or even a half a year. It would be interesting to see some team try this once they see things going South in the middle of a season.
In the Sox case, for example, Adam Dunn is truly only playing right now because of money. Most definitely you could trade him for somebody who would hit better than .100. If you didn't care about money at all, some other team would take the chance because Dunn has a big upside and it's all reward with no risk for them. On our side of the trade, we'd instantly have someone in the lineup with increased production. Now working this theory out for multiple players would be interesting and very tough to sustain, but even with one player, this could make a difference.