Congratulations on your Interview Invite! That's a great sign.
There is a bit of a question of how much you need to prep for your interview. If you need more than 1-2 days of prep, then I would do interview and prep as much as you can to make a great impression. That interview is a great opportunity and obviously they considered you even with your low score and you can talk about it in the interview that you were planning to take the GMAT but now that you got it, you will delay your GMAT and instead were preparing for the interview (that shows that you take the school seriously).
If you are decent at interviewing and don't need days of prep (which I feel most don't), I would take the GMAT before the interview. I think you have a very good chance to improve your score and if you do, you have a trump card to bring to your interview with you and say - I got a 700+ score. If you don't, I would stay quiet or you can still do the above argument and say that you are planning to retake in about 3 weeks.
What you have to think about is, can you pull off a stellar interview even if you bomb your GMAT or will it make you super nervous?
As to your question, the decisions are released on a certain date but the AdCom actually meets throughout the review process and they make decisions for 20-30% during each meeting, depending on how many meetings they have and they jointly review each candidate and then make a decision. Usually each candidate has a recommendation (Admin or Deny) and often people will have champions/advocates (interviewers) who will recommend admitting them despite a weakness in GPA, GMAT, etc. They will argue their reasons but the majority has to agree on that candidate that they will be a good addition to the program. What you have to do in your interview is provide a good-enough impression of yourself (don't worry about trying to look amazing, just be genuine and a good human being). But what you do want to underline that if you get admitted, you will absolutely choose this school and will attend. AdCom hates when people choose other programs AFTER they had to pull a favor for you, so they will be watching for those ques. Make sure you address that aspect (which I hope you honestly and wholeheartedly want to attend).
Good Luck!