Indeed, it makes me wonder if published code leads to higher citation counts.

Although if it does, I suspect it has more to do with the fact that there's a product & marketing around it.

I wonder if it's more subtle than that - if your paper has associated source code, then it's likely that people reading it might try it out, and the ideas that you've presented will stick around more than a short paper with no follow up material.

In other words, papers are only a short glimpse into your research, presenting code allows an interested reader to look deeper, and means that they're more likely to remember what you've done, and cite it later.