Viscous Coupler

It depends on how it fails. If the fluid leaks out, it will be like there is no rear drive shaft. You will have strictly front-wheel-drive.

If the coupler is binding internally, or locking up, you can have the front and rear drives locked together solidly, just like on a four-wheel-drive truck. With those, "walking tires" is caused when the rear tires make a smaller diameter circle when turning than the front ones do, but both axles are forced to turn at the same rate. This is why you never switch to four-wheel-drive when driving on clean, smooth roads. Four-wheel-drive is only used when snow, ice, or mud allows the tires to slip.

"All-wheel-drive" is different. The manufacturers specifically do not call your system "four-wheel-drive" because they want to differentiate between the two systems, and they do not want people to think you can go off-roading like you would with a truck. The viscous coupler contains two sets of rotating blades surrounded in a thick fluid. The fluid tries to make both sets of blades turn at the same rate, thereby transferring power to the rear wheels, but it allows some slippage to occur to allow the rear wheels to turn slower than the fronts, when cornering.

If something came apart and is allowing the two sets of blades to contact each other, the coupler could lock up solidly and cause the tire hopping when cornering, or the coupler might just chatter. How the failure progresses from there is hard to say.