FWIW, my $BOSS-2 had a PhD, loved LaTeX and even set one of our lower-level guys on writing all our company-internal docs in LaTeX. It actually worked out pretty well.
I imagine that an obviously-LaTeX resume (look for the ligatures, the correct spacing between sentences vice after periods, the clean, consistent grey across the page, the bold, clean margins) would play especially well with him. As you might guess from the preceding sentence, it'd probably play pretty well with me, too!
Good point, I fear it could backfire in a business setting. Mind you, I'm a huge LaTeX fan, but the one study I'm aware of that compared the efficiency of Word and LaTeX for a couple of average writing tasks came to a pretty damning conclusion (see quote below). So, I'd argue that LaTeX is the right tool for long math-heavy texts under version control, while better tools exist for most other tasks.
> LaTeX users were slower than Word users, wrote less text in the same amount of time, and produced more typesetting, orthographical, grammatical, and formatting errors. On most measures, expert LaTeX users performed even worse than novice Word users.
Because the point of a business card is to effectively signal your impressiveness.