If so, how deep?
Guess, just for guessing:
To have a positive effect, this auction would have to repeat the outcome of the previous one: a single winner, who can convince the market that he bought for a "good price" and does not intend to dump the coins.
However, that seems a bit unlikely, because:
* There are almost twice as many coins being auctioned this time, and twice as many coming in a few months.
* There seems to be much less excitement this time about those coins. (Last time, some even argued that those coins would have extra value as collectibles -- "the" coins from "the" Silk Road -- and/or for having been blessed by the US government. I have seen no such claims this time.)
* Therefore, it is more likely that, this time, there will be several winners.
* There is even a small chance that some lots will be unsold. (AFAIK, the USMS can ignore bids for any reason, including them being too low.)
* If there are several winners, some of them may remain unknown.
* If there are several winners, or unknown winners, or unsold lots, the market will probably assume that the coins were bought below market -- suggesting that the big players are bearish;
* If the market thinks that some of the coins were bought below market, it will fear that they be dumped for profit.
Moreover, the price increase after the previous outcome was announced only reversed the drop that occurred when the auction was announced. There was no such drop this time, so why should there be a recovery?
Thus, if I had to guess, I would guess "no effect, or a drop".