In answer to those age old questions....
Q: Is the Pope a Catholic?
A: Yes
Q: Do bears **** in the woods?
A: Yes
Q: Do the N7's own sockets work when the device is being charged via the dock?
A: Yes....
....to the extent I've tested it.
Scenario: Nexus 7 sat on dock, being charged via the mains, OEM cable plugged in to the dock. OTG cable plugged in to the N7's own power/data socket.
Mouse receiver plugged in to the OTG - wireless mouse works on the N7. Don't have a wired mouse, nor a keyboard (wired or wireless), but see no reason why either wouldn't work too. Whether you could run adapters for both mouse and keyboard, wired or wireless, don't know.
Flash drive plugged in to the OTG. Via Nexus Media Importer, jpegs and mp4's work fine. No audio unless a speaker or earphones are plugged in to either the dock, or the N7's own audio output. The N7's own audio socket does work whilst the device is being charged.
Dock plugged in to PC USB. N7 shows it's charging, but does not appear as an attached device. That said, I'm not sure why you'd connect the dock that way. You'd just connect the N7 directly via USB, no? You'd still get charging(albeit slower) , and can drag n drop in the usual way.
Haven't tried anything more. I'm retired so I don't have to worry about work type docs or sync'ing or any of that malarkey, just my own entertainment content. And that works fine. YMMV.
HTH.