Yes. If you have two-factor authentication or two-step verification enabled on your Apple account, you can sync iCloud with FullContact using an app-specific password.
NOTE: If you’re trying to connect from the FullContact for Mac app or the FullContact for iOS app, please make sure you’re using the most current version of our apps.
To create an app-specific password:
1) Go to https://appleid.apple.com/ and sign in.
2) Scroll down to Security, then click Generate Password under App-Specific Passwords.
3) Create an app-specific password for FullContact.
4) Copy and paste that password into the password field on FullContact when you connect your iCloud account.
You’re all set.