Depends, are you using gsync or freesync at all?
It all depends on the game and the monitor. There are times you can go over 144fps on a 144 herts monitor and nothing will happen. It really depends on how the game displays the image.
I have a 144hert monitor and only issue I ever had with any games was on CS:GO with over 250fps. For some reason in that game I wouldn't get ghosting or tearing but get display lag. I changed in console max_fps 144 and ever since then its been smooth as butter.
I've played a few other games that went over 144fps and didn't have those issues.
So long story short. If you see tearing or ghosting. Turn on Vsync, gysync etc... or set a max fps limit within the game or video control panel if possible.
But...