In general, Windows Safe mode is only about Windows, it has nothing to do with connectivity or...
It is a troubleshooting mode for Windows that loads a restricted subset of core Windows services, usually limited to the absolute bare minimum required to start Windows: only the absolutely critical applications, services, and drivers. The fundamental purpose for safe mode is to determine if there is something wrong with Windows (i.e., if it boots in safe mode the Windows problem isn't likely to be in the core, but possible in a driver application you installed. So from that perspective "safe" is not a reference to connections, but Windows, without anything else added or installed, works -- look elsewhere for the problem.
The other occasional use for safe mode is to get rid of something you can't remove any other way (e.g., can't delete, file in use by another application -- the other application isn't likely to run in safe mode, soooo.....).
Hope this helps.
David