I am using several widgets that switch languages between French and English, such as Testimonials, Tag Cloud.
Widgets to be translatable must be localized, if they are, they can be translated and switch the same as did the original plugin in my experience.
If no localization code exists in the plugin template, then no translation will show until that code is added. See plugin localization for that.
In the case of widget titles translation, I have used the title short codes successfully when title translation was not available such as for menus.