I wouldn't push for a GPU, the CPU is very limited anyway.
Two cores of 2Ghz will not play any modern game.
Would be better to get a CPU. A GPU will fit as this CPU requires only 6W of power and it's safe to plug it in.
As I see it, the PC uses SODIMM(laptop) RAM and it only has one slot for it, furthermore it looks to be a BTX motherboard.
Also, the CPU seems to be using a BGA socket, meaning it's soldered to the motherboard.
Would be best to try and sell this and get a new system for $300, with a Pentium G4560.I'll post a build soon.