Internet (WAN) connectivity is required for stack communications, such as licensing, security services signature downloads, NTP (time synchronization), and CFS (Content Filtering Services). At present, these communications can only occur through the Primary WAN interface. If you require these types of communication, the Primary WAN should have a path to the Internet. Whether or not the Primary WAN is employed as part of a Bridge-Pair does not affect its ability to provide these stack communications.
If Internet connectivity is not available, licensing can be performed manually and signature updates can also be performed manually (https://www.MySonicWall.com/).