This would be called an "active placebo" and would certainly be documented.
It's common to find controlled trials against an existing drug to demonstrate that the new drug performs better in some way, or at least is equivalent with some benefit like lower toxicity or side effects. In this case, using an active comparison against another drug makes sense.
You wouldn't see a placebo-controlled trial that used an active drug but called it placebo, though. Not only would that never get past the study review, it wouldn't even benefit the study operator because it would make their medication look worse.
In some cases, if the active drug produces a very noticeable effect (e.g. psychedelics) then study operators might try to introduce another compound that produces some effect so patients in both arms feel like they've taken something. Niacin was used in the past because it produces a flushing sensation, although it's not perfect. This is all clearly documented, though.