Are Automated Refineries/Extractors as fast as three workers?

Automated extractors harvest at the same rate as extractors that have 3 drones.

I tested this on the Hand of Darkness mission. I choose this mission because it ends at 5:12 if you don't kill the first hybrid and you start with drones and one extractor.

I was able to harvest a total of 696 gas by 5:12 with and without the Automated Extractors ability. Turning on Vaspene Efficiency allowed me to gather a total of 845 gas with and without Automated Extractors by 5:12.

Results

+-------------------------+--------------------+-----------------------+
| Total Gas Harvested     | Vespene Efficiency | No Vespene Efficiency |
+-------------------------+--------------------+-----------------------+
| Automated Extractors    | 845                | 696                   |
| No Automated Extractors | 845                | 696                   |
+-------------------------+--------------------+-----------------------+

Note: The mission starts you off with 100 free gas, so the net gain is 100 gas less than the totals I posted above.