Unless the 1060 can put out close to and around 100 FPS at settings and resolution you want, then there wouldn't be much point in getting a 144Hz monitor, unless you are going to buy a new monitor anyway.
Refresh rate and FPS go hand in hand, so there would be no difference in going from a 60Hz monitor to a 144Hz one, if the GPU were to still output a maximum of 60 FPS. It'll work fine, but the benefit of what the monitor is capable of, wouldn't be seen.
I recently bought a new 1080P 75Hz monitor. I did look at 144Hz models, but I don't play that many games. I'm not a serious enough of a gamer to spend the kind of money on a GPU that would have made getting a 144Hz monitor a good purchase. I still have a Rx470.