Would this mean that the trading hours for stock of companies listed in both NYSE branches would be extended by one hour due to time differences?
Roughly speaking, you will find the prestigious / big market cap / rich companies listed on NYSE main market, ETFs on NYSE Arca, small caps on NYSE American (ex Amex), and very small caps on NYSE National.
The listing requirements and prices, as well as fee structure also differ for each market. National has a fee structure to incentive adding liquidity for instance.
If the asynchronicity bothers you, imagine that you can also trade e.g. HSBC secondary listing on NYSE NY market hours + the ADR of HSBC HK on NYSE NY hours + HSBC primary listing on LSE on London hours + HSBC HKSE on HK hours for a lot of fun.