You can leave Wii Connect 24 on without problems. Nintendo cannot and will not secretly update your System Menu, and it doesn't conflict with anything that I can think of (except maybe older versions of Preloader). I leave mine off regardless.
You can safely enable WiiConnect24.
However, on modded and virgin consoles alike, it's probably best to turn off the "Standby Connect" mode, because it can cause overheating damage to the GPU.