Yes I'm pretty sure you're right about Emma Cooper being his bride. It adds up. At 15 she was working as a worsted spinner. my guess is that they would have met at Ackroyds where William was a dyer, before he joined the army.
I noticed that an Edwin Gaunt also married in 1904. The page I looked at though had 2 men and only 1 woman on it, so can't tell who he married. We thought they had both died as single men until the last couple days.
I did see an Emma Cooper Gaunt born 1908, but as she died in Manchester I can't really be sure that she is theirs.
Jill