With an aquarium, it isn't much of an issue, because the flow restriction is just not there.
With a rig, the load is well out of a pump's optimal flow range and so, you can expect your pump to draw more power, and heat up more.
A lot of people run their pumps 24/7, and don't report any problems.
If you want, the simplest way to shut off your pump, is to wire in a relay, so that the pump shuts off with your PC. It's a really
simple mod
You also have the option of adding a bypass button, in case you're working on your cooling system, and you want to turn on the pump without turning on the PC.
edit: you can also put in an outlet, on the backside of your PSU, so that you don't have to cut into the pump's wiring. Like
this
edit2: you can also use a solid state relay, instead of a mechanical one, for more reliability.