As the title says: does rendering with compositing passes enabled (depth, vectors, ambient occlusion…) slows down the render?
I believe it slows down render but very subtle that you shouldn’t worry about it.
Where it can really slow down rendering is the saving of each of the passes. Especially if you are using a large format like tiff or exr and have a slow HDD or network.
Saving to .exr can be significantly faster than .png.
Smaller file sizes with compression too.
The reason for using OpenEXR is that this format was designed – by Industrial Light & Magic, no less – as a lossless data exchange format. All of the information produced by the render will be saved in its exact arithmetic glory: “here are the actual numbers, exactly as I computed them.” The only “compression” that I am aware of is simple run-length encoding, to avoid the obvious waste of literally storing “thousands of consecutive zeros.” 
“MultiLayer,” then, is an extension that was pioneered by The Blender Foundation(!), and quickly adopted by the industry. It allows the various “layers” of data produced by the render process to be conveniently stored together in one file. (One wonders why ILM didn’t think of that first …)
“Image file” formats, per contra, were engineered for a completely different purpose: to allow images to be rapidly but acceptably displayed on very cheap hardware. The audience is the human eye. Therefore, these formats are only suitable for final deliverables. They were never conceived to be “intermediate process files.” While OpenEXR specifically was engineered for no other purpose.
Anyway – if you’re doing multi-pass renderings, always(!) use MultiLayer OpenEXR for all stages up to and including the “final prints,” which can omit the MultiLayer bit. Now, produce all of your various “deliverable files” from that same OpenEXR gold-master. Do all of your format-specific and display-size specific steps only now. This delivery step will now become the first and only step in which the data is “encoded” or where any “loss” occurs. Always produce each deliverable directly from the master – never from another deliverable, because “noise” adds-up very quickly.
Don’t worry about how big the files may be nor how long it takes to write them. External hard disk drives are now dirt-cheap. And, go ahead … “if you might need to use this-or-that layer, ask for it to be produced and included.” Splurge …