BAD idea.
Coatings eventually fail or have 'pin holes' that allow 'wicking' (by capillary action) of fluids. The 'water' that enters 'behind' the coating will rapidly become 'de-oxygenated' (O2 uptake by the base metal to continually restore the chromium rich surface) and RAPID an d 'enhanced' corrosion will occur.
300 series Stainless Steel needs to always be exposed to an 'oxygen-rich' environment to maintain its 'rust free' characteristics. If you 'coat' and the coating 'leaks' you very rapidly accelerate corrosion.
If you need to 'protect' a stainless shaft, then a thin coat of bottom paint will suffice as most 'bottom paints' are 'oxygen permeable'.