First, I think you're already making those connections. You're a real person to your readers, not a faceless "big publishing company". That's all that's really needed here. Whether one does that through a blog, a twitter stream, Facebook, or personal appearances and signings is irrelevant – the key is being viewed as an individual rather than a faceless entity.

Second, I'm talking about using those personal connections (or even just the potential for them) converting that sub-segment of your readership who would (or has in the past) pirated your work. That number's far smaller than the entirety of your readership.

Or put another way, I think even the Pirate Bay might [1] respond differently if an individual asked them to take down a work because it directly impacted feeding their family, rather than a lawyer demanding they do so. None of the "legal threats" they have up (and have ignored) are from the actual content creators.

[1] Maybe they would ignore it because TPB has an ideological axe to grind; I think the principle is sound, even if it's an extreme example.