The easiest way to do this is to create a bus, insert the distortion and the gate in the bus, and configure the side chain to the gate from the unprocessed channel.
In my example here I have a guitar track. I created a bus and inserted distortion then gate. The sidechain to the gate comes from the unprocessed guitar track. Then the send to the distortion occurs after the sidechain. Does this achieve what you want?
Optionally you can make the side chain and the distortion sends pre-fader and then silence the unprocessed track.