I can only tell you what happened with my class that graduated on June 29th.
SWO's got something like 14 days before they reported to their ship. Some guys, since they were single and had nothing else to do reported to their ship the week following graduation.
SNA's got 3 months of OHARP.
The NFO's in my class only got a month of OHARP I believe.
Supply people, their school was down the street from OCS so they didn't get OHARP.
IWC folks (Intel, IP, etc.) we all got 3 months of OHARP.
Everyone else (sub-nukes, CEC, EOD/SEAL) I believe they were given a few days for transit time before they had to report to wherever they were going.
Again, this is just what happened to the people in my class and may not be the case for everyone. Keep in mind, even if you don't get OHARP you can take leave depending on your report date to your next command. Leave will start that day following graduation and continue until you report to your next command or OHARP station so don't take your sweet ass time doing either unless you want to burn through all your leave.