Yes, the tub can be reglazed even if part of enamel is gone.
Best not to relaze it yourself. It will cost more if you don't do it correctly and have to have a professional re-do it. It can be difficult at times to remove the glazing, however, it can be done. Any time I have to remove the old glazing, then I charge more.
You would need to spray it on, not roll or brush. The product can only be purchased at or thru a company. It can also be dangeours to spray, you need safety equipment.