Yes, agree with this. The overall long-range direction that the fishless cycle will push is downwards. This is because the end product of nitrite(NO2) being transformed into nitrate(NO3) by the N-Bacs (nitrite oxidizing bacteria) is a couple of hydrogen ions (H+) as well as the nitrate ion (NO3-) and some of those plus ions will manage to link up with the negative ions and form HNO3, nitric acid, a strong acid which will push the pH in the acid direction.
In tap water, some of the mineral content can participate in reactions that neutralize the acid effect but as they do this, they get used up. As OM47 mentioned above, if your pH was able to move easily up a whole point from 7.4 to 8.4 just by the addition of ammonia, this may indicate that not many of these "neutralizing" minerals happen to be available in your water. Thus it will pay off to make pH a regular (although not necessarily daily) measurement along the course of your fishless cycle. As you get on the lower side of 7, the fishless cycling process will get slower and slower until about 6.2, where you may not see any progress at all. As OM47 wrote, at some point when the pH gets down there, a large water change will remedy the situation.
~~waterdrop~~