Many AI-based code assistants, particularly those powered by Large Language Models (LLMs), provide complete solutions, which can reduce active problem solving and limit incidental learning, the acquisition of knowledge as a byproduct of task engagement. Such learning requires active participation rather than passive acceptance of AI-generated answers, which might be incorrect. This study examines how incidental learning can be supported through guided interaction. We present LeetCoach, an LLM-assisted coding platform that applies a cognitive forcing strategy, prompting learners to reflect and take incremental steps instead of receiving full solutions. Using LeetCode-style questions, we conducted a pilot study with novice and advanced college programmers who completed tasks under assisted and unassisted conditions. Novices showed substantial post-test gains despite receiving AI guidance only during the intervention, suggesting that incidental exposure improved later performance. Advanced learners showed smaller gains. Across both groups, participants required fewer debugging attempts in the post-test compared to earlier stages, indicating improved debugging efficiency and algorithmic understanding. These findings provide early evidence that LLMs can be designed to promote indirect learning while shaping problem-solving strategies. This work offers a proof of concept for cognitively informed tutoring systems in computer science education and discusses implications for integrating LLMs to enhance both immediate outcomes and lasting skill development.