It depends a bit on the system hardware. Going to make a bigger difference the slower the system is. Higher core count CPUs will have resources to spare, and as long as you aren't hitting system memory limits that should be a minor change.
Also have to factor in the monitoring software and its polling rate. Is it logging? Or just displaying data that is running through the system anyway.
Easy enough to test on something. Pick a benchmark, record the scores a few times. Then do the same with the monitoring tool of your choice running and see if there is any detectable difference. I suspect it is a very small difference and possibly within the margin of error.