Yes, but the effect can be less pronounced on low-quality source footage, and also can be much less pronounced on footage that is largely unchanging, for example a long locked-off shot of a still-life type object with little or no movement.
One of the primary reasons for making multiple passes during compression is to better analyze the media and to make further optimizations to the compressed data. This can lead to smaller files and better overall quality. VBR encoding in general benefits from its ability to "borrow bits" from scenes that have less motion or detail, in order to spend them on scenes with high motion or detail. When a compressor makes 2 passes (commonly one internal CBR pass from which analysis data is gathered, and then a second pass to generate the actual VBR compressed media) it should generate a higher quality output from most typical video media.
Your mileage will vary based on your source content, compression settings, and so on. But generally speaking, you should be getting higher quality footage (when comparing with 1 pass of an identical bitrate) out of a 2 pass compression.
Here's a great article at IBM that discusses multi-pass encoding for MPEG-2 content intended for DVDs:
http://www.research.ibm.com/journal/rd/434/westerink.html
Notably, you can see the chart at the bottom which shows a flat-out SNR (signal-to-noise ratio) comparison between both CBR and VBR 2-pass compression.