I am running Legendary Heroes with an AMD Turion 64 TL-64 and ATI HD 2600 graphics, which is considerably older than your E-350 rig. Also, only 4 GB of ram installed/3.2 GB or so addressable (32 bit Windows Vista assigns the upper memory addresses to video card memory and other such thiings, so part of my ram is left unused). No issues to speak of.
I had no significant problems with Fallen Enchantress either, btw.
Your E-350 should do fine, as long as the video drivers are properly implemented in this game. As I'm using WAAAAY outdated ATI drivers thanks to Toshiba not releasing an update for them, and ATI Catalyst not allowing me to update them (tells me to go to Toshiba), I think you should be fine, and probably have a nicer looking experience than I am having on my older machine (which still looks pretty good all things considering).