Yes, conditioner can do this. Part of it is that it will separate out ammonia if you have chloramine treatment and ammonia is a mild base. Of course, during fishless cycling you have the added ammonia shooting the pH upward a bit and that's even more significant than the conditioner usually. But conditioners vary and some of the weird differences in them is the reason I like Prime for the cycling period. Also keep in mind that the cycling process itself will eventually exert an even stronger downward force on pH if the water is fairly low mineral content.
Your worry about the conditioning of water for water changes during standard weekly maintenance after you are cycled and have fish is unfounded I believe. What stresses fish is if they receive an unduly large change in mineral content (hardness) and not pH (pH is often confused in the way because changes in hardness will -cause- pH changes) and the conditioner, while it may change pH some, is not changing hardness. By the way, stresses to fish from hardness and pH and water changes are generally greatly overblown, when in fact stress from traces of ammonia and nitrite are much more serious and damaging. Doing a good fishless cycle and having a really strong biofilter is much more important than any kind of water change stress usually.
~~waterdrop~~