That would not make any sense, because the mining difficulty is very high at the moment, and that means there is a much greater cost to produce a single coin.
From the analysis I've seen, most miners would not be able to produce a single Bitcoin at a cost less than seven hundred dollars, so it does not make much sense to expect people to dump the coins in the market at that price. As you said, anything is possible, but I think the only event that could lead to such a price drop would be serious technical problems on the network.