I don't see anything wrong with being AFK ingame. I mean, it's not like there weren't enough slots for everyone or something. And I don't see the point of farming online time, since it has absolutely no use. I don't think mods activity is assessed based on online hours. As far as I know, only ban count is relevant.
I personally stay minimized ingame every now and then, especially when I'm doing something else on the PC. I keep IRC open, so I get notified on new reports and I simply have to maximize. If I don't respond to the report, it means that I'm temporarily away from keyboard for any reason, not that I'm not interested in responding.
I think the advantages are overwhelmingly more relevant than disadvantages (if there is any disadvantage at all...)