I think you may easily have seen similar sentences. In short, I trust you when you say you have.
In your context both are possible and mean the same, more or less.
Sentence one makes more sense when you think of the time and act of adding the person - specific past moment known to you.
Sentence two emphasises the current relevance of what you did - the person is now in the e-mail conversation, whatever an e-mail conversation means.
For more information you may read some of the literally hundrds of threads we have on present perfect vs. past simple. You may find that similar questions have already been asked by some several hundred... thousand people before you.