Fps limits are set by the cpu, resolution and details is mostly gpu. My i7-3770K is strong enough to get 300fps in CS:GO and my gtx970 (equitable to gtx1060 at 1080p) can get ultra at that fps (65% usage) So a 144Hz monitor is no worries. At 1440p the i7 is still capable of 300fps,but that 970 now has to fill @1.7x as many pixels so won't get 300fps output at ultra, I'd have to drop details to medium or live with @150ish fps output.
The difference is noticed in games like my modded Skyrim (138 2k/4k/8k mods) where there's enough scripted code added that my i7 (55% usage) is only capable of 59-60fps. The gtx970 easily handles that graphically at ultra, 4k DSR and still gets 59-60fps. Dropping to 1080p medium settings still gets 59-60fps. Cpu bottleneck, 60fps limit. That would be an issue on a 144Hz monitor, monitor refresh doubling gpu output, use of free-sync or G-Sync would be a bonus to smooth gameplay.
Cs:Go is easy on a pc, not requiring much for 1440p@144Hz. Question remains though is if you can live with the harder cpu/gpu games suffering as a result. Witcher 3 is brutal on a cpu, even a 9600k and at 1440p@144Hz is not going to get good results on a Rx580, although will be smooth with free-sync, you'll be looking at closer to 80-100fps at high settings. You'd need a 2080 to get ultra at that fps and a 9700k to get closer to 120fps.