Richard, John is absolutely right.
The history you have to date contains too much conjecture. You NEED the documentary evidence only certificates can give you, whether it s to prove or disprove a connection.
I strongly urge you to get the birth certificate quoted for Alfred, also the one for Letita (Camberwell 1889), and that 1903 marriage I quoted.

I hate to say it, but to me, until those documents prove otherwise, it seems highly possible your grandfather and Letita ran off to America leaving his wife and children behind.