I do not think so. Would you think and say that the Bitcoin market on Bitstamp is directly connected with the ETF market in Wall Street? They are 2 different worlds, one can go up and down without affecting the price of the other.
Every investment product (e.g., an ETF) is directly connected to the asset it invests in (e.g., Bitcoin).
Your analogy is flawed. Bitstamp is an exchange. Wall Street (i.e., the NYSE) is an exchange. Both serve as a marketplace for different things. They're not connected. Your analogy doesn't apply to the Winklevoss ETF, which trades on Wall Street, and Bitcoin, which the those ETF trades on Wall Street are seeking to buy or sell a piece of.
If the Winklevoss ETF is investing purely in Bitcoin (no hedging, no additional securities or commodities included beyond Bitcoin), when Bitcoin goes down so will the Winklevoss ETF.
This article explains what these guys are trying to do with their Winklevoss Bitcoin Trust.
https://moneymorning.com/2016/11/08/a-winklevoss-bitcoin-etf-guide-for-investors/.Now, you can employ trading strategies with the ETF that will change the correlation which YOU and YOUR trades have to Bitcoin, but it doesn't change the direct correlation the Bitcoin ETF will have with Bitcoin.
For example, with any stock or ETF you can choose to buy and own shares ("a long position"), you can buy an option contract to purchase shares in the future at a set price ("a call"), you can buy an option contract to sell shares in the future at a set price ("a put", a "naked put" if you don't already own the shares), you can enforce combinations of calls and puts ("spread strategy", "straddle strategy"), you can buy shares using a loan ("a trade on margin"), etc. These are strategies available to any investment that trades in the stock market. And if the Bitcoin ETF becomes part of the stock market, these strategies will also be available.
I hope this helps clarify my comments. I'm happy to answer more questions.
This ETF will connect some investors on Wall Street to Bitcoin. It allows greater demand, which should raise the price for everyone. The important part is that this ETF likely won't be available to just anyone, you'll probably need to be a qualified investor ($5m in net worth, $1m in investable assets).