If my Pyke, Returned and a friendly unit die in the same showdown, do I still get the gold due to Pyke's backline?

No — Backline doesn't earn you the Gold here; a friendly unit dying isn't a trigger for Pyke at all, and if Pyke dies in the same cleanup as the enemy unit, he misses it.

Backline only changes damage assignment order: your opponent must assign lethal to your other units before they can put any damage on Pyke (Rule 826). It doesn't stop him from dying and it doesn't generate Gold. His ability is "when an enemy unit dies while I'm at a battlefield," so your own unit dying is simply not an event he cares about.

The real question is timing: combat damage is dealt simultaneously, then all lethally-damaged units are killed in one Combat Cleanup. If an enemy unit and Pyke both die in that cleanup, Pyke leaves the board at the same instant the condition is met and "sees" nothing — the same precedent as Viktor, Leader (Rule 383.2.c.2, FAQ #13129). You only get the Gold if the enemy unit dies in a separate action while Pyke is still at the battlefield, e.g. you kill an attacker with a spell before combat damage.