1 - there is no such thing as 100% pure water, even triply distilled water, or the purest Millipore water has some ions / contaminants.
2 - Kw (water equilibrium (heard of it?, then apply Le Chatelier's priciple; remove the H+ and there will be made more of it from OH-, as well as water will split back up in H+ and OH- to resupply the concentration of these 2 ions)
so answer is very easily: NO
To change pH add acid or base, like sodium as Dan said