I'm thinking to design a Grails web application UI using the Polymer library, as it provides custom templates, data binding and helps to reuse web components on any page. Also it is pure HTML, so server side processing should be reduced, as compared to JSP or GSP pages.
So, my question is, will it be a good approach for a large application and also performance, browser compatibility and code management etc.?
Everything that means to organize and reuse your code is great for large and complex web apps/projects, and you can achieve that with web components (in this case, with Polymer).
Its performance is good as it provides features like HTML imports, which avoids duplicate requests to the server (and you can also use libraries like Polymer Bundle or Vulcanize to package your assets in production).
Polymer features are supported natively in Google Chrome and Opera, and partially in Firefox, Safari and IE/Edge. You can have a full browser support with polyfills (webcomponents.js).
And code management with Polymer is great as it encapsulates element's styles and templates. In conclusion, Polymer and web components provides great tools and features to work in a large project and they have a great community behind.