Is there a way to include a small survey on the Event Planner Registration?

That feature is already in the product. It is found here:
Event Planner
EDIT
Edit Event
Edit Activity
Look for this section:
Registration Questions

Registration Questions -- Classmates will answer these questions during the registration process.

Question Answer Type Active Edit Delete

Add Custom Registration Question

Then click the "Add Custom Registration Question" to add a new question.
Remember to save the changes and then click the "PUBLISH>>>" button to make the new changes visible to classmates.