Not Day Z but it might on Arma 3. Still, the bottleneck shouldn't be huge, it's still a triple core. And besides, anything over 60 FPS is pointless, since normal monitors can only display up to 60.
First gen Athlon II's biggest problem is the criminally low quantities of cache, other that that, it's a great lil CPU.
Edit: These CPUs overclock quite well. If you don't want to, you could always try to unlock that extra core and see if it's stable.