Multicore rendering increases the frame rate, but it also increases input lag.
I ran two tests comparing multicore on and off. The first test I did was with max_fps set to 1000. With multicore rendering on I hovered around 800 fps and with multicore off I averaged around 400. With multicore enabled the input lag ranged from 5 ms to 21.7 ms with an average of 12.3 ms. Multicore disabled ranged from 1.7 ms to 21.7 ms with an average of 12.1 ms. The difference at such high frame rates is fairly negligible, but enabling multicore does add a small amount of input lag.
I lowered max_fps from 1000 to 144 for the second test. When the frame rates are equal it becomes very apparent that multicore rendering adds input lag. With multicore enabled the input lag ranged from 5 ms to 26.7 ms with an average of 16.4 ms. Multicore disabled ranged from 3.3 ms to 23.3 ms with an average of 12.8 ms. It is still less than a 4 ms of additional input lag, but it is a significant percentage and will be higher at lower frame rates.
If you are limiting the frame rate and have enough power to reach that limit only using one core you should definitely disable multicore rendering. If you have a much higher cap than a single core is capable of it may be worth enabling multicore rendering to get a higher frame rate over the increased input lag depending on what is more important to you.