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I think that it is possible for the art market to continue doing business without the auction house but I do not think it would manage as effectively (or lucratively). Buyers and dealers would have to put much more of an individual effort into finding the art that they wanted or patrons to sell works to. The auction system is very convenient for most of the parties involved and keeps the art market moving at a swift pace. It would not be in the interest of these parties for the auction houses to disappear, and I believe this is a significant reason for the houses coming out of the scandal relatively unscathed.
I I think it is interesting that with all the discussion of antitrust law , is ironic when the power held by these two auction houses really amounts to a monopoly to begin with. As they are, I do not know that Sotheby's and Christie's would meet the criteria of open competition as defined by the Sherman Antitrust Act. For example, antitrust law was used recently (and successfully) to block AT&T from acquiring T-Mobile in what would result in the narrowing of the cellphone market to three main providers which would decrease competition. If this is the case for the cellphone market (as well as many others), how can it be that only two auction houses are allowed to influence/control the art market unchecked?