I would recommend you get everything up there asap. If they don't have to ask for further information then your car might move faster too. I'm under the impression that when applying online you may not hear back from a co at all, if you have them everything they need they may not contact you till your Visa is granted.
So get everything up there, if you don't have a medium, book one and give them the email for your booking. Then at least you know if you don't hear back it's sort of good news too because they have everything.
If your immi account says "assessment in progress" it means the case has been opened and someone is/will be looking at it.