No the private key is not in the manifest.  This key is used by the Manifest
utility to sign the files included in the manifest.  The public key must be
put in your app.config of the application using the UAB.  Here's an excerpt
from the UAB documentation:

"The manifest utility also includes public/private key generation
functionality. To create a public/private key pair based on the RSA
algorithm used by the RSAValidator provided with the Updater Application
Block, select Generate Keys on the File menu. The keys are saved as XML
files, which you can copy and paste into the manifest utility's Key text box
and the application updater file. You should paste the private key into the
manifest utility's Key text box [my words here - used only to sign the
files, it will not become part of the manifest], and the public key into the
application's updater file."

Thanks,

Sam