I don't have direct experience, but even if it does work, be careful to note that you may or may not be paying U-Haul directly. I rent a storage locker, and the company also has a U-Haul franchise. Even if I were to rent a U-Haul vehicle from them, it just shows up as "Jim Bob's Storage". According to the Visa supplier locator, they code as "Business/Professional Services".

Here is the link for the supplier locator: https://www.visa.com/supplierlocator/search/index.jsp