Hi Allan,
No, I don't believe them to be related, at least not directly. My grandmother was the descendant of Glenn (Glen) Afton Izett (1879-1940), Jane and James Izett's second to youngest child (Two others died).
As for William, here is a possible connection. Scotland census April 3, 1871, for Blythswood registration district of Barony (644/6, schedule 105, house 14, Gayfield Street). James Izett, joiner or carpenter, head, 29 years and Elizabeth his wife, age 29. Their children were James, age 8; Annie C., age 6; John H., age 5; Alexander H., age 3; and William H., 9 months. All of the family were born in Lanarkshire except James [the Emigrant] Izett who was born in Burn, Dalry, Ayrshire.
BTW, my 2nd cousin, Glen, was the compiler of this data. Hope this is a help.
Paul