I think it unlikely really.
I know I am repeating what has been said but trying to reason this.
William is not with his wife and family in 1911.
His son William is 8 yrs old in 1911 and believed his father to have been killed in 1915.
We think it unlikely that dad would have been a soldier due to age.
Did young William have any memory of his father being at home?
When did his mother die? Did he remember other family events?
We do know that a relative, also called William, was killed in 1916. Maybe confusion of names 
I have tried to look for any W T in hospitals or asylums but not yet found anyone.
At the moment, I can only think that the youngest child’s birth certificate might help as suggested but even then William might have been named as father.
William Turner (b) 1903 his mother died in 1944
I have no idea about if he knew the whereabouts of his father I had no reason to ask him really
All I remember him talking to me about was his father dying in WW1 and his own occupation down the mines
My Grandfather died in about
1986 so memories of us talking are fading now I'm afraid
