Abhishek19932601:
Mixed feedback on your thinking:
Yes, going from a 690 to a 700+ GMAT would be an important jump. Of course, the bigger the delta the between the 690 and your ultimate score matters too. A 690 to 700 probably won't change much, but a 690 to a 730 would be considerable.
No, I don't think applying in R1 this year (compared to R2 last year) is going to give you a major advantage. While it is possible that applying this upcoming year will be marginally beneficial than last year (given the abnormal competition), the reason why people move up in ranking is because they have meaningful changes to their profile. A new GMAT score is one. Others include a major promotion, change in job, new outside accomplishments, important recognition/award, etc. - you get the point.
While "luck" does play a factor, it's not enough without those changes to warrant giving up what you have now. You are also talking about a big jump. The top 10-15 is much harder to crack than below top 15. I don't want to dissuade you from going for your dreams, but I do want to shed light on how this process generally works.