Well I think using a pH of 7 will be fine, it's just that using a pH of 6 would be better.
Alkalinity (which is measured as pH) determines the availability of minerals in water that can be absorbed by your plant. For example, at high acidity or high alkalinity, certain minerals may become unavailable to your plant. Therefore, it is beneficial to keep your water at a pH that will allow maximum absorption of nutrients.
For soil grows, this pH is around 6-6.4. Watering with this pH allows your plant to easily absorb the buffet of minerals that it needs.
So in terms of how long it will take: as soon as you water.
Also of importance is the pH of the soil. Some soils are more acidic/alkaline than others, so you will have to balance the pH of your water to the pH of your soil. An easy way to do this is to make sure your (soil pH + water pH) / 2 is about 6.2.
On top of that, as you continue watering, your soil's pH will change depending on what you've been watering with. So take a test every few weeks. The more you water, the closer your soil pH will get to your water pH.
Hope this helps.