There is no Code requirement to pigtail the receptacle hot and neutral unless you are using a multiwire branch circuit. (A circuit with multiple hot wires) Even then, the requirement is that removal of the device cannot break the neutral so the neutral has to be pigtailed but not on a two wire circuit.
300.13 Mechanical and Electrical Continuity — Conductors.
(B) Device Removal. In multiwire branch circuits, the continuity of a grounded conductor shall not depend on device connections such as lampholders, receptacles, and so forth, where the removal of such devices would interrupt the continuity.
There is a Code requirement to ground the receptacle in such a way that it does not break the equipment ground. Either you can use self grounding receptacles or you can pigtail the ground.
250.148(B) Grounding Continuity. The arrangement of grounding connections shall be such that the disconnection or the removal of a receptacle, luminaire, or other device fed from the box does not interfere with or interrupt the grounding continuity.
Ok all that said, you don't need to ever have two cables in a conduit unless you plan to run two circuits. You cloud then conceivably have two cables protected by one conduit and with 12/2 that you would need for 'a 20 ampm circuit I wouldn't try that in anything smaller than 3/4" EMT.
Good luck and stay safe!