Yes, just about all conditioners have a chemical which will convert ammonia (NH3) into ammonium (NH4+, aka ionized ammonia.) Examples are Aliphatic Amine salts, hydrosulfite salts or sodium hydroxymethane sulfinic acid.
[This function is totally separate from that performed by Sodium thiosulfate (Na2S2O3), which is the typical chemical used to perform the removal of chlorine or the splitting of chloramine into chlorine and ammonia and the removal of just the chlorine part.]
And you are correct that if you had a little ammonia in the tap water and if you had a working biofilter, then the "ammonia to ammonium converter" would buy you a short period (about 24 hours, as you say, may be about right) of time for the bacteria to do their work and eat this newly added ammonia/ammonium.
In fact, one of the big problems we have among beginners is not realizing how short this time is and confusing it with the function a working biofilter plays. "Ammonia to ammonium converters in conditioners" can't substitute for a working biofilter. Their action time is just too short for ongoing use.
The best choice of conditioner for a given individual hobbyist, like lots of products, depends on a number of personal factors. Maturity of the tank and experience of the hobbyist can and perhaps should be the primary factor. The newer the tank and the less experienced the hobbyist, the more payoff there is for choosing one of the best conditioners. As these two factors change, the payoff becomes less.
Like a lot of hobbyists here I recommend Seachem Prime to new users because it has a record of handling both cycling and various difficulties like ammonia converting better than many other conditioners. Amquel+ seems to be another conditioner that gets good reviews, but may be limited to US hobbyists. The other plus factor for Prime is that it is nearly as concentrated (perhaps fully as concentrated) as some of the pond dechlor products that folks use to cut costs. A couple years out, after the biofilter is mature and the hobbyist more experienced, a choice of a cheaper pond dechlor or a change to more frequent smaller water changes with no dechlor may work out, especially if cost is an issue to the hobbyist. Otherwise, a slightly more expensive but pretty concentrated product like Prime may stay as the best habit. Of course, a beginner not knowing even to use a conditioner is worse than the choice of conditioner!
Whew! Time for me to make like a fish myself and get some swimming exercise! Luckily for you guys that'll make me shut up for a bit

!
~~waterdrop~~