Set the “multi pass” to “Depth” only and you get only this pass as result written on the disk.
To save time you might switch off Textures and Lights. (If you need the Alpha information from some objects in the Depth Path (not available in older versions), you might leave textures on. (Render Settings >Options.) Check Reflections, refractions, etc. It is all not needed for that. (make a new render setting for that)
The Depth information is sometimes relatively fast rendered in this way, but if your scene contains a lot of complex animation, all of that might be needed to be calculated again, if not cached in the first place. No need for GI either. You might know better what is in you scene and what is not needed for the depth pass anyway, just go one time along the Render Settings>Options.
Certainly switch off Anti Alias. The depth information is a measurement, not an image information in the first place. To get nice results the common practice is to render in double size, scale up the footage in question and scale after it down. The quality is much better. I know that some people argue other wise, and that since the ‘90s…
So, I would say the answer is yes, C4D can render a single pass. I would love to get a Dollar for each wrong answer in the web…
Have a good one