tldr; Yes & No, Mostly No.
Depends if you use VSync.. If you use it, Yes, definitely. The game only calc's mouse clicks each frame that you run. 144 is double that of 60, so better timing opportunities.
If you don't, then it just depends how many frames your pc pushes. if you're running 300fps, The timing of your mouse is negligible. I run at 120 fps just cause I see no point in rendering frames I won't see. (The benefit of extra frames is why i push double my refresh rate)
You could also argue the fact you'll see more of the movement you're making at 144, it'll give you more chance to time them better.