Yes.
Maybe.
Effect of Watering Devices on Performance During Pullet-Rearing and Cage-Laying Phases of Single Comb White Leghorn Hens
By W. B. ROUSH and G. D. BOGGAN
"...Birds tend to prefer passive, open drinking systems. Richardson (1969) indicated that when birds are given a choice between drinking water from an open system such as a trough or a closed system such as nipples that there is a tendency for the birds to prefer the open trough. It was noted that the total amount of drinking activity over 24 h is greater when using a nipple than when using a trough. Birds drink in fairly dis- crete " b o u t s " ; these bouts contain more drinking responses in the case of nipples (up to 100) than troughs (rarely more than 30). Presumably, the birds were exhibiting a difficulty in meeting satiety for water from the nipple drinker.
The engineering design of manufactured watering devices affects the availability of water to the birds. Activation of the nipple drinker used in our experiment required the bird to push up on the water valve to obtain water. Zanforlin and Xausa (1982) noted that chicks used in their experiments had difficulty in pushing up the nipple valve and picked laterally at it. There are commercial nipple drinkers on the market that have been engineered for 360°lateral activation by the hen...."
That was long ago - 1987. Maybe nipples are easier to use now.
Or maybe it still matters - measurably if not enough to not recommend nipple waterers in commercial buildings.
This 2014 study
https://www.scielo.br/j/rbca/a/YWRZmLJWmGZpWHMffysjrDJ/?lang=en
"The objective of this study was of evaluate the influence of different drinker types on the egg production, water intake, mortality, poultry litter relative humidity, egg weight, eggshell percentage, and egg specific gravity of broiler breeders. The experiment was carried out in a commercial farm with 37- to 44-wk-old broiler breeders. A randomized block experimental design, consisting of two treatments (bell or nipple drinkers) with four replicates of 4.000 females each, was applied. ...Birds submitted to nipple drinkers presented lower water intake (p<0.05). There was no influence (p>0.05) of drinker type on egg production or mortality. Poultry litter relative humidity was lower (p<0.05) under the nipple-drinker system. Birds drinking from bell drinkers produced heavier eggs (p<0.05) between weeks 39 and 40. Hens drinking from bell drinkers laid eggs with higher specific gravity and eggshell percentage. It was concluded that nipple drinkers can be used for broiler breeders during lay."
I haven't found any studies comparing open water in containers larger than cage cups to anything else. That matters in at least some other species.
Or any studies about backyard hens in winter conditions - whether they drink enough more to for better blood circulation to prevent frostbitten combs. Or, the other side, whether the increased moisture in the manure causes more problems than the increased hydration prevents - it wouldn't in a properly ventilated coop, I think, but there are a really lot of badly ventilated backyard coops.
My conclusion, so far, is that nipples vs open water matters for hydration but only a very little.