A friend of mine has an emachines et1331g-03w. The poor guy runs CS:S at 15 fps. I told him I might be able to salvage what he has, and maybe we can. All he wants to do is run CS:GO at 40+ fps on 1280x1024, low or ultra doesn't matter, it beats 640x480.
My problem is no matter how much I google around, I can't find out the wattage of the PSU or what open slots the mobo has for a GPU. He doesn't have much to spend, maybe $80. (stretchable) At first I recommended an antec basiq 350 and a radeon 6570, but with my limited knowledge of his computer and building in general, I wasn't sure if he had a PCI-E 2.1 slot or not. Maybe PCI-E's are backward compatible. I wouldn't know. All in all, I want to know if an upgraded PSU is necessary, and what graphics card can fit in there.
If you want, you can just open the case and look at the power supply. If it has at least 15-16a on the 12V rail I would say it would be able to run a 6670 DDR3, which are usually pretty cheap, around $60. It seems to have 6GB of RAM, so that's good.
The Athlon X2 isn't that slow of a processor. I used an X2 215 and was able to game on it and what not with a 6670 DDR5. The DDR3 is slower, but not that much.
I haven't been able to find out if the motherboard has a PCI-e X16 or not. If it does, th 6670 should run fine, as in almost all cases PCI-e is backwards compatible.
emachines are NOT known for sticking a "Quality" PSU in their Box.
That said, the 6670 is a VERY low power card, so even a 250/300 Watt PSU should handle it. Would only add about 50 Watts max to current power drain.
And to answer your last question, yes, overloading a LOW quality PSU can cause damage to the system. A GOOD PSU would just shut down if current drain is to high, NOT always true for a "good" PSU, BUT much more likely with a low end PSU.