Intuitively, I would say the two sentences are somewhat different in meaning. With 得 you frame the interview positively, so you could alternatively translate the sentence as "Tomorrow I still get to have an interview" which implies that you are happy to do the interview. Whereas without 得 you frame the interview neutrally/negatively, i.e. it could imply that you are not looking forward to the interview.
Example:
如果你坐定定,可能有得食糖啊!("If you sit still, you might get to have candy/a sweet!")
With 添 at the end, as you rightly mentioned, suggests the interview is additional on top of something else, so the sentence with 得 might imply that 'the other thing' is good, whereas without 得 might imply that it is not. However I'm not sure how these bits of colloquial language might be formalised in terms of linguistics/grammar terminology.