Unfortunately, the ui:include tag will only embed Facelets components, not entirely separate webapps.
Embedding a webapp in the the page view of another webapp can be a problem. The simplest "brute force" HTML way would be to use frames, but frames and JSF are not very good friends, so this can mean some struggle.
It's always good in cases like this to consider whether a Portal approach is what you really want. JSF does support working in a JSR-288 Portlet environment.
Customer surveys are for companies who didn't pay proper attention to begin with.
I misread the question. If the OP wants to embed a completely separate app, then portal technology seems apt.
Unless a facelet component with a backing bean, invokes the app, packages up the generated HTML and presents it.
This of course leads to all sorts of css, js, image reference issues and is not a trivial task.