I wouldn't say that liquid chlorine has
zero effect on pH, but it has zero
net effect -
over the whole chlorination cycle. Adding bleach will raise pH, the following use of chlorine (disinfection, oxidation, UV-decay) is an acidic process which will bring the pH back to where it started once FC is back where it started (ignoring other effects on pH).
Within normal maintenance bleach additions, you hardly notice a thing. For example, if you bring your FC from 6ppm to 8ppm (i.e. lower target FC range to higher target FC range for CYA 50, covering a typical daily FC-loss of 2ppm), then (assuming TA 80ppm) pH will rise from 7.6 to 7.7 - hardly noticeable in a drop test. Once FC is back to 6ppm, pH will be back to 7.6. Often, the bleach effects are hidden behind the pH-drift by aeration.
But when doing a SLAM, the pH-rise by adding larger bleach quantities is very noticeable (at least with a pH-meter, drops tests won't work anymore at SLAM-FC). That's why it is important to lower pH before starting a SLAM. And again, once the SLAM is over, pH will get back down to where it started (plus pH-drift by aeration that occurred in the meantime). In above example, adding enough bleach to get FC from 6ppm to SLAM-FC of 20ppm, would raise pH to nearly 8.6.
Here are a few references to chem geek posts about the effect of bleach on pH, and the whole
cycle being pH-neutral:
Will a digital pH meter read accurately at high chlorine
Worry about PH after adding liquid chorine
Equations for Chlorine Chemistry