Early language development, and vocabulary size specifically, is a predictor of well-being later in life, such as emotional development and academic achievement. Many successful vocabulary interventions for young children involve sharing a book with a caregiver, because storybooks are a good source of vocabulary that one might not otherwise encounter in everyday life. With the advent of Large Language Models (LLM), automatically generating stories has become a feasible way to tailor materials to the needs and interests of individual learners. Here we evaluate 1) whether parents of preschoolers find automatically generated stories containing specific vocabulary target words acceptable, and 2) whether preschoolers can learn these target words from being read the automatically generated stories. We find that parents overall consider automatically generated stories engaging, age- appropriate, and educational. In addition, children successfully learn the target words in the storybooks (compared to control words drawn from books not read). We conclude with a discussion on future work to improve the effectiveness of automatically generated stories to support robust vocabulary learning.