Can I set Wootric up so that a survey appears only after specific actions have occurred?

Yes, you can defer triggering a survey until you determine that your users should see one. This is called conditional triggering. While you cannot do this in our user interface, you can do it by making additions to the code.  Here is an example code snippet that you can customize.

Some things to consider when setting conditions:

If you set the survey to appear immediately after the conditions are met, you will bypass the survey sampling settings in the interface.  Any changes made to the sampling rules in interface will not work.  You will have to apply any changes to sampling after the fact, directly to the code.