If I train a dweller's abilities, then breed them, is the boosted ability considered for offspring? From how the game mechanics work, I feel the answer is "yes", but it goes against how real-world breeding works so I am curious if someone can confirm this.
The two parent dwellers do have an effect on the offspring's stats but not significantly. Common dwellers' starter stat threshold is 2 points so the child will inherit the most common high stats of each parent but only to a max of 2. You have to train them to increase their stats further after they've grown up.
e.g. If the two parents have high stats in perception and different stats in other fields, then the child will grow up and have the max threshold in perception, two. Think of it as a child inheriting a family name and continuing family profession.