It shouldn't. Charity Engine can run continually in the background of any modern PC without the user even noticing. Any other task has priority, so Charity Engine only uses the CPU - your PC's 'brain' - if nothing else is using it.
(So, using the example below, if your PC was using more than 60% of its CPU then CE would be suspended.)
If you do notice a slowdown, Charity Engine can be turned down, set as a screensaver-only, suspended or switched off with a mouse-click. It also has a scheduler, so you can set it to activate only at certain times of day.
You have total control over it at all times.