We saw our Connection object works with the FakeServer but does our acceptance test finally pass now? Not yet. We still have to provide a server there (fake or not) and we still have to finish the implementation of the client.
Acceptance tests are meant to verify that the software really does what we wanted once it's in the hands of our users. For this reason, it's usually a good idea to limit the usage of test doubles in the context of acceptance tests. They should work as much as possible by reproducing the real usage of the software.
While mocks, stubs, dummies, and so on are rarely seen in acceptance tests, it's pretty common to see fakes in that context too. As fakes are supposed to mimic the behavior of the real service they replace, the software should notice no difference. But if you used fakes in your acceptance tests, it's a good idea to introduce a set of system tests that verify the software on the real services...