Don't bother unless you were planning on upgrading your monitor anyway, and you're very serious about shooters.
I upgraded from a ancient budget-tier 1080p144hz TN with no g/free-sync to a mid-tier modern 1080p240hz IPS with free-sync [AW2521HF]. Even with all those factors, it was still a bit tricky to justify. No regrets though.
Speaking to 240hz specifically, I can subtly notice the additional frames as the feeling of "like slow-motion but played in real time". Don't expect a directly observable improvement to aim. I could be hitting slightly more, who knows. Admittedly I also kinda like the peace-of-mind that I'm not missing out on anything.
If you do upgrade, I heard that DyAc on the 240hz Zowie monitor XL2546 slaps. Optimum Tech made an intriguing video on it: https://youtu.be/np--4AZxUBg