If she is deaf, pups can learn hand signals for commands just as well as people can. She can still be trained, you just would have to make sure she is looking at you, same as with a deaf person.
Not all vets do the tattoo. Mario was neutered May 2015 and he is tattooless. If you believe it is a good idea, maybe you could ask the vet prior to the surgery to do the tattoo. Then if they do not by normal practice, it is something they can look into and may change their normal practice
Good luck and may you have many happy years together.