Yes, app still works if you use a different (non-gmail) email; but CAUTION!!!! I did exactly that. I set up a new, independent account on MY email server specifically for this app to connect to, to backup my phone SMS/call logs, etc. This was literally the only app/client using this email address; and this app of course knows the password for it. So, after a while my dedicated account was being used to send SPAM and my domain and IP because blacklisted until I figured out it was this account being used to log into my server to send the SPAM. The ONLY explanation is that this app's publisher has a way of gathering non-gmail accounts and passwords and either using them or selling them to SPAMMERS. Perhaps this is one reason why Google won't approve them to use gmail accounts. Anyway, BEWARE!! I suggest you do not use this app.
I set up a new, independent account on MY email server specifically for this app to connect to, to backup my phone SMS/call logs, etc.