Adding an outlet above this metal box
Electrically, you can go either way

Attaching to the push connector or attaching to the backstabs or screws is 3 of one, half dozen of the other.  

I mean, backstabs (and push connectors) are known to be unreliable, so you take your chances of having an hours-long, frustrating bug hunt.  Screws are more reliable, but you must torque them adequately. 

A better option might be to switch to a screw-and-clamp type receptacle, which can support 4 wires in special grooves under its screws (2 per screw).  Assuming Code allows this; the choice of push connector for 2 wires is an odd one since there are already 2 receptacle backstabs.  I suspect there may be a local amendment that requires the push connectors and pigtailing. 

Cablewise is a different problem

This appears to be modern construction using steel sheathed AC cable instead of non-metallic.  Note how there are no grounds in the box; those are on the AC cable and secured by the AC cable's clamps.  

Nobody uses AC cable instead of Romex for no reason.  This is certainly due to a local amendment requiring it.  This means you also need to use AC cable or proper EMT conduit. 

The problem is your cable needs to go upward.  The two upward holes in the junction box are already occupied.  This means you will have to come into the bottom and go upward, or relocate one of the existing cables to side or bottom if possible.