Does Titanium Backup backup the Signal private Key?
Signal 4.17.0 introduced encrypted backups. This is the preferred migration path. Also the Titanium Backup route does not work in current releases.



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I just tried this and it worked flawlessly. 

After restoring Signal on your new Phone you should re-activated your connection by unregistering and re-registering to the Signal servers. As of now you can do this in the Signal Settings > Advanced tab by toggleing Signal messages to de-activate then re-activate [1]. In this Process you will have to re-verify your phone number and you'll have to reconnect your Signal-Desktop clients afterwards. 

You won't loose your Private key or your Signal-Desktop messages though.

[1] https://support.whispersystems.org/hc/en-us/articles/213190487-Why-is-there-a-delay-in-receiving-messages-