Student or Learner
If somebody asks me "Would you like to share your email with us"?. Is it correct to say "I don't have an email address"?
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
In addition to your suggested response, you could say "I don't have one". It's becoming more and more unusual for someone not to have an email address at all these days.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.