Will a DDR3 work as it should work on a DDR2 motherboard?

ok well ram and graphics cards have different interfaces,

the current graphics card interface is pci-e 16x so you should be able to fit any pci-e graphics card into your machine given sufficient power supply, so whether the card itself has ddr5 chips on it or whatever doesnt matter.

ddr2 is a ram standard, and ddr3 is the latest version, you can not put ddr3 into a ddr2 slot, it just wont fit.

if you arent sure whether your new upgrade will work, please give us more details on your motherboard make and model, your power supply make and model and the upgrade you want to make, and someone here will let you know if its compatible.

DDR < DDR2 < DDR3 < DDR4 < DDR5

G is just there to indicate it's for a graphics card

actually that is wrong, GDDR architecture's are completely different to DDR architecture's.

This thread explains pretty plainly: Graphics memory speed is not bounded in any way by your motherboard. If you had the right interface, you could put a GDDR5 equipped GPU on a motherboard that only supports PC100 RAM.

As it was already stated graphics cards don't matter. Any motherboard can support any graphics card ram (GDDR) doesn't matter what the motherboard is.