At this time, there is no Address Book feature in Adobe Send, but there are two alternatives for accessing your Address Book.
You can use Adobe Send through Adobe Reader, and in this mode, you have access to your computer's address Book. For more information on how to use this, see https://forums.adobe.com/docs/DOC-4611.
The other option available to those who use Microsoft Outlook on Windows is the Outlook plugin for Adobe Send. Note, however, that the Outlook plugin doesn't currently support the sending of Personalized links.
There is a limit of 250 recipients for a single transaction.