Pidgin still notifies me when buddies come online, even though I'm set to "Do not Disturb"

"As already pointed out, Do Not Disturb does not turn off notifications. If you want to do that, go to Tools > Plug-ins (or Ctrl+U keypress) and uncheck the 'Libnotify Popups' plugin that is responsible for the notifications. Enable the plugin when you want to re-enable notifications again.

You can also choose to configure the conditions on which the plugin provides popup notifications. One of the conditions is ""Only when available"". Check if selecting this will stop notifications when you set your state to anything other than Available."