1. Yes. It is needed to indicate that the action will be done (because it becomes a thing of past) -- translates to "No matter if you are coming or not, I will BE GONE" which is stronger than "... I will be going".
2. 盡管, 不/無論, 任憑, 別管, 管他三七二十一, 不問好歹
3. 管你說甚麽, 我會去的 or substitute any of the above words or phrases.