With HD 620 refresh rate is the wrong question. It's not even close to powerful enough to drive a 144Hz gaming monitor with any game more demanding than solitaire.
Minimums.
1080p 144Hz - GTX 1070
1440p 144Hz - GTX 1080 or even a 1080 Ti
4K 144Hz ( I think there are a few now ) - GTX 1080 Ti x2 in SLI
That doesn't even take into account the laptop CPU not being capable of driving any of those cards.
I don't think they even make a monitor with a 144hz refresh rate at lower than 1080p resolution.