GBTC has started trading with no affect on market price...yet. Only been 2 days. Next significant date seems to be may 18th when NASDAQ Stockholm begins trading xbt provider which says they will back all shares bought with bitcoin. Seems like this could have a much more immediate affect on price. Volume will also be waaaay higher to start.
GBTC can't influence the market, anyways. The volume is much too low in order to do that. First of all, it's more of a long-term asset, anyways, and secondly there aren't many people who are actually eligible to sell their shares. GBTC was created by using a "loophole", anyways. A real ETF that is buying coins on the open market will make things pretty interesting, I presume!
I think this opening phase of a few weeks or a few months is the predictable time to test the waters and let larger orders keep outbidding themselves and when the volume does pick up, by a few larger shareholders willing to sell some or all of what they hold, then they could take the shares they sold at 2,3,4,5x current bitcoin market price and start buying coins on the open market and drive the price up. So, I haven't seen the data about what the average shareholder holds in BIT but I'm sure that there's plenty of holders w/ the equivalent of 4 and 5 digits of bitcoins. If they're able to get 2,3,4,5x for their shares or more then they can do that much more damage while scooping up coins on the open market, perhaps.