No, a lack of minerals is not a bad thing in a PC water-cooling system. The higher the concentration of dissolved minerals, the more chance you have of developing deposits on various wetted surfaces that will reduce heat transfer and in some cases restrict flow.
When talking about the various types of purified water, remember to keep it in the context of PC water-cooling. Plain old grocery store distilled water (RO filtered, steam distilled, uV treated) is excellent for PC water-cooling systems. The only other thing you probably need to add is some type of anti-corrosion additive.
Using demineralized (demi), deionized (DI), or ultra pure water in your PC won't hurt anything - BUT it won't gain you anything either. Process equipment (boilers, incubators, etc) that require a constant flow of feed water can be quickly damaged by DI water as it will leach out the metal ions. This does not happen in your PC because it is a one-time addition and then that same water just gets recirculated. IF you were continuously passing DI water thru your water-cooling system loop instead of recirculating it, then it would quickly start dissolving components.
Paying extra money for DI water vs. distilled water doesn't gain you anything because it has such a high affinity for ions it will quickly become un-deionized (and basically the same as distilled) by the time you get the system filled. DI water will immediately start sucking ions out of the air (disolved gases), the bottle or container you pour it into and your cooling system. But the amount of ions absorbed in a one-time fill are so miniscule they do no measurable damage - it takes constant, continous use to do permanent damage. Unless specially handled and sealed DI water quickly becomes ionized.
Good links BTW...