This is an interesting point you raise here: Do Open Source programs have to be pretty inside? Sometimes you have a really capable program, which does its job very well, you use it, recommend it to others, but you better not look under the surface, as the source could make you blind.

I know which project you are talking about here, because I use it frequently, and when I wanted to replace the home-spun referrer-scanning logic for my blog (code I have to update all the time to keep up with all the different search engines) with something more complete, I looked at above source to see if I could use some of their code for that purpose. And yes, I also recoiled in horror (and gave up). Totally monolithic, horrible from a software engineering stand-point.

Would this be a better project if its code was more modular, with components useful outside its primary application? Yes. But is the reverse also true? Does a useful program become less useful because the implementation is ugly?

I was trying to find a web-log-analyser tool with nice pictures for the PHBs, and google pointed me towards a site on sourceforge, where a well-documented tool was available in perl, with all the nice graphs management likes.
I will now go on my way and find something better or (yuck) do it myself. Pity - it did look promising, and I am lazy and impatient.

I would not do that, especially when you are lazy and impatient. Your PHB is not going to look at the source, the project is, as you say, well-documented, popular and works as advertised. Just treat this open-source project as closed-source (for your own safety).