Eligible for Dropbox; first available appointment is in June.

[F12H1]

Hello,
I am currently booking my visa appointment and I am eligible for the dropbox program. I am on the payment page currently and realized that the first available appointment is June 2nd 2016 for Mumbai.
I will be flying to India this week and scheduled to be back in the US in first week of May. Since I am eligible for the dropbox program would the June 2 date be not applicable to me?
In a worst case if I am called in for the interview would it mean that I have to be in India till June 2 or later?

Please advise...


Thanks,
F12H1