I'm only working with DC, so I assume that it will just not let current pass. No?
In the simulation, do you see DC current passing through the cap?
If you remove the capacitor completely, it should do the same thing. There does not need to be any current between a MOSFET gate and source for the transistor to remain on, indefinitely. When the switch is open, the gate is floating. Whatever charge has last been left on the gate will theoretically remain there, forever, unless the simulation includes the gate leakage of the FET. Maybe I don't understand the simulation, though.
This is one way to test if a signal or logic level FET is working, out of circuit. Take your multimeter and put it on diode test. Put one probe on gate and one on the source. Then lift the probes and change the meter to continuity test; put the probes on source and drain to test continuity. Do the diode test again, but reverse the probes on the gate and source. Then repeat the continuity test. One outcome will show continuity, because the FET gate is saturated. And the other will be negative, because the gate is below threshhold, and the source to drain will be high resistance (or will have a diode drop, if the probes are reversed... still negative continuity test).
In the diode test, there is a voltage (typically about 3V) applied through the probes, but limited to only a small current. This will charge the gate. The charged gate will retain its state long enough for you to do a continuity test, if the FET is out of circuit.
**I bet this is what MasterTech's video demonstrates.