Yes and no. audio|acacia runs best when it is both connected to a network and connected to the internet, but can run without either under certain conditions and with limited functionality. Below is an explanation of when network/internet connectivity is required/used.
For Front-End Controllers
A connection to the internet is required for initial downloading of the user interface. Once loaded, the user interface is run using HTML app cache technologies. This means that you can open and close the user interface without needing to be connected to the network or internet. When connected to the internet, the user interface updates itself to the latest version automatically. However without internet connectivity, no online metadata or album artwork will be available.
For Back-End Servers
A connection to the internet is required during startup. This is so that the software can perform automatic updates and a network license check. Once running, no network or internet connection is needed. However without internet connectivity, no online internet streaming sources or metadata will be available and without network connectivity, no network connected sources or speakers will be available. Only those located on the actual device.