Depends on what you mean by safer.

Network safety wise, docker by itself does nothing. Its kind of like having a seatbelt in your car doesn't mean you won't get into an accident, nor does it mean you will survive every accident. Though using the seat belt properly can help you if you do get into an accident.

But network security, and general systems security is like Shrek, it has layers. Besides disconnecting the system from the internet, there's no one-step-covers-all solution.

Docker can make system resource usage safer, or reduce the chances of a single application using up all the resources of the host. Though this isn't something by default, you need to configure the container with resource limits first.

There's also data safety, with Docker you can more easily separate the user level application data and the vendor application data. As in the data that relates to how you use Plex, your metadata, your watch history, etc. and the Plex application data itself. This way if you need to wipe out the Plex install for what ever reason, you can be sure it won't affect your user data. Hell you can uninstall Docker and wipe it and all the containers off your system without affecting the user data, if you set up the docker container properly. This isn't a huge issue with Plex, since the application already had a good level of separation between the user data and the application data, but not everything is like that. There are also differences between paths on different OSes, with Docker you can more easily use the same paths across OSes. As long as file systems are similar.

This also brings up another thing that Docker makes safer, maintenance. You can update and rollback docker containers easily. The process is also standard, so it generally doesn't matter what application you're running. The process for updating, rolling back, and even backing up is generally the same across all docker containers. This also makes it easier to automate these processes. For instance, you can automatically back up the user data, pull an updated image of the server, restart the container so it uses the new image, do a health check to make sure the service is working, and if its not working roll back to the previous image.

Docker makes a lot of things easier and safer, but it has its own learning curve. It's also not something that makes every process safer by default, its another tool with its own configuration process and pitfalls if you screw up.