What does this "..." mean in emails? For example,
"Mike...You are always welcome to come to our social event."
Because they do not know proper punctuation? At first I thought you were asking about the use of quotation marks but now I understand that you mean the ellipses, correct?
I don't know that there is a real reason for this. In my opinion it is a less formal punctuation than using a comma after "Mike" but it is in no sense standard.
The alternatives may seem too formal, (comma) or too imperative (no punctuation after Mike) so the ellipses "..." is a way to "soften" the tone in a friendly way.