Not necessarily, but realistically - Yes. You can run an open case and keep the radiator outside the case, but I don't think this is a desirable long term solution. The alternative is to use a tub of water rather than a radiator, but if space or portability is an issue, this is not going to work. Plastic blocks are also coming on strong. These are usually small units that are used for transmission or oil coolers.
Submersibles require an additional element - a water reservoir.
An In-Line pump requires no reservoir. Water Pumps are typically those used for small fountains and aquariums. The higher the cfms, the more noise. Let's assume you are interested in better cooling and with less noise. If you are really not that handy, then go for a complete system - water pump, water block, fan and radiator.