It will run the monitor yes, but don't expect to game at that resolution with it.
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The RX460 can run most esport titles at 1080p medium-high settings. As for most recent triple-A titles you're going to have to settle for medium settings at 720p for playable framerates.
Altogether your system is not a good match for your 1440p monitor. The FX4300 + RX460 combination will struggle with many of the most recent titles at 1080p, and the included CPU heatsink will prevent the CPU from reaching its full potential.
As a compromise, I would suggest purchasing a cheaper 1080p monitor, then spending the difference on upgrading your GPU to at least a RX 470. That way you would at least be able to enjoy the visuals while playing with medium-high settings at 1080p.