If it's got low ram then there's a fair chance it will. It really depends on the game though. If it was originally made with DirectX and ported to OpenGL it'll likely have worse performance.
If you plan on using Wine then you'll get much worse performance.
in the case of TF2, it runs natively on linux. however, i'm unsure if there's any way to use it on dx8/9 or something. unsure what it even uses.
the computer also has like 2GB of ram, so that's something.