WordPress gets constantly updated and every update brings new features and fixes bugs.
Will the plugin no longer work with a WordPress version that is no longer supported?
No, if the plugin worked in the past it will most likely work in the future. Sometimes features not available in this version will cause an error that no longer gets fixed. Also, there’s no dedicated test for the deprecated version.
In general, I recommend keeping your WordPress site and its plugins up to date to prevent security vulnerabilities.
Read more about updating WordPress.