No, you don't. The unit connects to the mobile device via Bluetooth.
However - you will need to connect to the internet to sync recipes created on the desktop web account to the app so you can brew them or if creating the recipe on the mobile device itself so that it syncs to your account.
You do not need to do this immediately before the brewing starts - you can do this the day before if you need to be prepared. It will be sitting there waiting for Brew Day.
You will also need to connect to the internet to sync your completed brew session back to your account.
This doesn't have to be immediately after. Just your next opportunity to connect.