Absolutely, the stock clutch has springs (most DD clutch disks are sprung, reduces the shock to the drivetrain) I'm unsure if it has 6 though. I can check in the mourning and report back Monday night.
You can shift a tranny into any gear without a clutch while it isn't moving. A clutch just seperates the transfer of motion to the transmission.
Here is my stock clutch, but you can't get a great idea of how many springs are there.
As you can imagine if the clutch wont engage fully then the motion can't be transfered over without some force. I'd put money on it that you could tap the starter with the car in gear and it would jump forward (if in a forward gear) even with the clutch to the floor. If your clutch pedal has a good amount of pressure (stock feel) then your hydro. system should be ok, check and see if your clutch fork is moving from the center point of the window (on the bottom of the tranny) when you press in your clutch. If all this checks out then it points to the clutch install.
See here to show that even a stock clutch disk can be used with an aftermarket pressure plate. The pressure plate is what would determine a majority of how much torque a clutch can handle. The disk does play a part but not as large as the pressure plate. Maybe this will also help you out.
Howstuffworks "Fly Wheels, Clutch Plates and Friction"
DISCLAIMER -
I DO NOT SUGGEST THAT YOU TRY STARTING THE CAR WHILE IN GEAR AS IT MAY CAUSE DAMAGE TO THE CAR OR MAY PUT OTHERS IN DANGER.