No, this feature is not available in Adobe Send. There was a feature in SendNow that required the recipient to sign in with an Adobe ID in order to access the file, but this is not a feature in Adobe Send.
Note that the file itself was not password-protected, and once downloaded by the recipient, could be forwarded on to others. If password-protection is important, I would recommend that you use the protection features provided by the document authoring tool (for example, Adobe Acrobat for PDFs or Microsoft Word for .doc files).
I am not a techy. How do I enable password protection in a PDF? Do I have to purchase that feature?