You'd be fine. Webstorm will create a .idea directory in your project, which will contain all the Webstorm specific project settings and configuration. But anything else is stored in regular ol' files you could edit with anything. I use Webstorm and my other teammates use VS Code or Sublime.
The only thing that might "break" is if you rely on Webstorm's tools for things like test runners, compiling, minifying and bundling code, etc, instead of learning how to do it on your own. You'd then need to learn how to set it up yourself with the command line tools instead of a nice GUI.
I create a project. There are two things they could do:
1. Make an ant/maven/gradle repo, and have the build command run gradle build or something.
2. Create a commandline (open source) tool called "intellibuild" or something, which reads the project files and does whatever the "build" button does.
Unfortunately, they don't do either, so if I don't have a license (or I want to give my code to others who don't use IntelliJ), my J2EE is not buildable.