I would postulate that you would probably be able to use an Athlon X2, as long as it was the one that shipped with series of machines..Any CPU with a later launch date would probably entail a BIOS update, which eMachines would not provide.
eMachines upgrades, as with most prebuilt computers, mostly center around more memory, and more HDD storage. Sometime it is possible to upgrade the video card, but the PSU needs to be changed at the same time. If you're looking for some immediate improvement in gaming, that might be the way to go. That being said, this is a slimline case, (?), and would not really cool very well in heavy graphics & CPU usage situations.
Unless you have access to parts on the cheap, you might at least give consideration to building a new machine.