Using Process Builder or an Apex trigger, Simple Survey can update fields on related objects, but it cannot display the current values of those fields on the landing page. For example, you can create a picklist for preferred contact method on the Survey object and copy the value to the related Contact, but the Simple Survey landing page renders before the value can be copied from Contact to Survey.
This is an example using Process Builder to update a picklist on Contact with the value of a picklist on Survey.
1. Create a process and select Survey for the object, and select when a record is created or edited.
2. Criteria checks that the value on Survey and Contact are different.
3. Cross-object field update.