Generally, Round 1&2 students are asked to accept/reject the offer and pay deposit by 4/15. But the exact date varies from school to school. Round 3 students can get back to the schools sometimes in June.
Ususally the Round 3 decisions won't be released until late March or even later (last year, some students didn't hear from the schools until May/June). So, advantage or not, I am not very sure. Besides, the chances of being admitted are slim in Round 3 because most of the seats have been filled in previous two rounds.