This is an interesting question. Readers would probably not consider Sergeant Major Morris as a holy man. There is very little that suggests this in the text. The very fact that Sergeant Major Morris gave the monkey's paw, knowing how dangerous it could be, suggests that he might be an unholy man.
However, if you had to marshall evidence that Morris might be a holy man, you can say two things.
First, he spent time in India and presumably got to know this old fakir, who is called a holy man. From this we might conclude that Morris is holy by association. Here is what the text says:
‘An old fakir put a spell on it. He was a very holy man and he wanted to show that fate ruled people’s lives, and that to interfere with fate only caused deep sadness. He put a spell on it so that three separate men could each have three wishes from it.’
Second, Morris also used the monkey's paw, and it seemed to have worked, even if he does not say how things played out. This might point to the fact that he has experience in the supernatural. Some may construe this as being holy in some sense.