You'll need to prep the surface and repair the crack before any coating is applied. Applying a paint coating would improve the bathtub's appearance. If this is an older bathtub, I'd highly recommend you start with a 3M Instant Lead Test Kit to know what type of paint you are working with and wear appropriate PPE if necessary.
Correct surface preparation is critical to the success of the painting project. Clean the surface thoroughly with an abrasive cleaning product to remove all transparent body fats and soap deposits on the tub's surface. Pay special attention to the edges against the wall, around taps, plug hole and handles. Rinse off with clean, warm water and repeat as many times as necessary to ensure all build-up is removed from the surface. Take some120-grit sandpaperand sand the edges of the crack and the areas with small surface cracks. You'll then need to sand the entire surface of the bath thoroughly to remove all shine. Use a fine grade of wet and dry abrasive paper (240 - 320 grit) and pay special attention to difficult to reach areas and the plug waste if you plan to paint it. Rinse all surfaces down and allow to dry.
Take some Selleys 50g Aqua Epoxy Putty Knead It and mix it as per instructions. Apply it into the dry crack with a Craftright 50mm Joint Knife. Make sure to push it as deeply as possible into the crack and smooth the surface off with the scraper. Once the putty has fully hardened, you can use the 120-grit sandpaper to remove the excess putty and then 240-grit to smooth, ensuring the area blends in with the surrounding areas. Ultimately, you shouldn't be able to feel the repair by running your fingers over it. Our sense of touch is about the same as sight. So, if you can feel it, you'll see it.