Does WebStorm have any built-in support for Internationalization and Localization?

Do you mean .properties files support (syntax highlighting, etc.)? No, it's only available in Intellij IDEA (https://www.jetbrains.com/help/idea/2016.3/properties-files.html)

Yes something like the properties files. Do you know if there are any plans of implementing that in WebStorm in the future?

No, I'm not aware of any; if you miss it, please feel free to create a feature request in youtrack, https://youtrack.jetbrains.com/issues/WEB, to let other users vote for it

Thanks for the info