Do you mean just during registration? When the user next logs in, would you want to re-import their profile information but not their avatar?
If you want the profile, but not avatar on returning logins, JFBConnect doesn't currently have a setting for that, but we can tell you a quick modification to the jomsocial profile plugin to do it. If you don't want to import any information during returning logins, there's a setting already for that called "Always Import Profile Data".
Let us know!
Thanks,
Alex