Can it handle a 144hz monitor? Yes your system will support it, but you wont be able to run modern AAA games at 144hz. Older games it will do much better, but the RX 480 is really a 1080p/60hz card.
With that being said, for a pcgamer I would not go get a 60hz panel in 2018. For one thing they are not that much more. And I would get a 144hz monitor as monitors tend to last longer than other pc components. So you may not be able to push 144fps today, but one day you may.