Please clarify, your question in the subject is asking if publicdelegates = send on behalf which is yes.
However your question in the post is asking if publicdelegates is the same as the attribute of Send As which is no. Not all Exchange store level mailbox permissions map to AD permissions. There is Exchange level permission send-as which does map to AD permission
send-as but there is not a publicdelegates permission that maps to a AD permission.
James Chong MCITP | EA | EMA; MCSE | M+, S+ Security+, Project+, ITIL msexchangetips.blogspot.com