Rack Extensions require active Internet connection at least once, when you access the Reason Studios Shop (or your account pages) and download/install the Rack Extensions on your machine. However, after installation it's possible to write your Rack Extension licenses to your computer and/or to your Ignition Key and run them without an Internet connection.
Trial licenses are online-only. Once you have purchased, you will be able to write the license to your computer/Ignition Key.
Note that using Rack Extensions with the Reason+ service requires Internet connection at all times.