They do. And I guess that manual operation is possible, but it's rather an emergency option only.
Fully automated docking for Soyuz capsules called Kurs[1] was developed in 80's for flights to Mir. When USSR dissolved and it turned out that this system was fully owned by Ukraine, Russian space agency tried to test how viable is to dock via manual bakup docking system TORU[2], which failed and damaged the space station. On the other hand, there is at least one occasion when Kurs failed and the manual backup saved the docking.
You’re understating the TORU mishap a little. Apparently they still needed KURS to get rangefinding and telemetry from the Progress supply craft, but KURS interfered with the signal for TORU so they shut it off and tried having a guy shine a laser rangefinder out the window at it instead. That didn’t work so they just tried to eyeball it instead, resulting in the crash which destroyed an expensive space station module and forced the crew to scramble to save the station from depressurizing completely.
