Can I use the survey to send my users down different paths based on their answers?

No. There is currently not a way to use the survey widget to divert a user to a different page based on an answer. The survey is essentially a means to collect pre-defined data.

You can drive some users to one section of your app based on a response. This can be done by creating a question as a text element then placing two buttons with the answer options defined on the button, for simplicity let's say they would read "Yes" or "No". You can link those buttons to different pages, but that user data would not be collected in your survey data. In our analytics, however, you would be able to see how many views that corresponding "Yes" or "No" page had.