Should I put a water-repellent coating on the inside of the windshield?

Generally no. Rain repellents and glass coatings are designed for exterior glass, where airflow and wipers remove beaded water. On the inside, they can cause uneven fogging and streaking and may affect visibility. If interior fogging is the problem, a dedicated anti-fog product and a thoroughly clean inner surface are the appropriate solutions. Products meant for exterior glass can also leave a film that is very hard to see in daylight but obvious under headlights at night.