branded computers does use other hardware then it's own brand. I know you already know this.
eMachines seam to only use third party hardware and only make their own cases and laptops full with third party hardware.
They choose vare cheap brands and hardware to make their products. that's why they are soo chip.... and crappy.
I doubt that they have chosen a PSU with upgrade potential.
If his PSU is this the following, the new card will not work
COOLMAX V-500 500W ATX Power Supply - Newegg.com