Would be better at what exactly?
Monitors can't show more frames than graphic cards have sent to them.
And the main advantage of any high-frequency monitor is that you can see more updates of your enemies' positions when they're moving thus you have more time to react.
And what will you react to with your 165 fps on a 240 Hz monitor better than you would on a 165 Hz monitor? You will get an update for what you see only every 1000 ms / 165 = 6 ms, and it will be 6 ms no matter if it's a 165 Hz monitor or a 9999 Hz monitor, because guess what - your monitor shows what your GPU sends to it, it can't make up anything on its own.
So when you see some cool number on rtings, e.g. input lag - make sure you check if it's input lag with the number of fps YOU have. Otherwise there could be no advantage at all for you from buying that super cool monitor that your GPU can't even fully load. Because "lower input lag" is not always the case when it comes to using your high frequency monitor at lower framerates.
That's why no, you wouldn't still notice the difference, but you might in some cases with some monitors, to know what exatly cases - check proper reviews.