In short, Yes. Hydrow uses an electromagnetic braking mechanism for resistance, so it always needs to be connected to power.
It is possible to row on Hydrow at default resistance without an internet connection. However, nearly every other feature of Hydrow requires internet connection. This includes the basic features of "Just Row" Mode.
We very strongly recommend using Hydrow where a strong internet connection (Wi-Fi or Ethernet) is available. Without internet, Hydrow's handle will still have resistance so rowing is still possible. However, the screen will have no functionality at all without a data connection and this type of use will not provide a satisfactory user experience.