Does caucus have any influence over selection?
No. They tend to stay out of selection processes or remain neutral supporting all candidates equally after Nikki Kaye beat List MP Jackie Blue in the Auckland Central selection of 2008.
In theory the Prime Minister could get involved in selection and he could sway things, but this would be highly unlikely. Like every other caucus member the PM has to work with the successful candidate, so aggressively supporting an opposing selection candidate is not wise.