Moving to Codeception from Behat and still getting used to it's concepts & where things go.
In the hypothetical that my tests are 100% driven from .feature files, does this mean that all of the test code could be in Contexts? That there wouldn't be anything in any functional tests that extend PHPUnit_Framework_TestCase? (Assuming that all my functional tests would extend that)
Codeception is not driven by Gherkin as Behat is. If you are moving away from Behat you will write functions in classes in Codeception directly and you are not going to start from a Gherkin script to then derive the executable specs (in your contexts files, page objects).
In brief the two flows
Behat
Codeception
The above is a very simplified description as your question is also very generic. I hope it answers your question