In Android Framework there is a string.xml file that houses all the strings for the application.
This allows for easier re-use and possible internationalization. My question is, is there any precedent/good reason of doing this in a web application?
When I have seen this done is has been for reasons you've already mentioned:
This allows for easier re-use and possible internationalization.
The argument for if it is a good idea or not depends on your target audience. Is it acceptable that all of the visitors on your website reading it in one language? (Not that browsers will attempt to translate as well.)