Scaly piscine
Cricket Web: All-Time Legend
Vettori averages 39.97 in Australia and goes at 2.91 an over. Australian pitches generally offer very little to finger spinners and the margin for error is very small so he'll definitely be milked at times. He's not a front line option. I can't realistically see NZ scoring the sorts of totals that will put Australia under big scoreboard pressure, they're probably capable of 350-400, decent but when you see Martin and Vettori are going to bowl more than half the overs there's not going to be much pressure.Vettori can trouble Australian batsman, he has done it before. Also, more importantly he can tie up one end.
Getting to the bold part, by picking 6 batsman and then having Vettori at 7 can put pressure on Australia if New Zealand bat first.
Honestly though, according to you NZ are completely rubbish with the ball and have absolutely no hope, I don't really know what you expect NZ's fourth seamer will do?
Even if you come across the one pitch that helps finger spinners in Australia, Vettori won't do jack on it anyway. If NZ want to take wickets they need 4 seamers and make sure none of them are called Chris Martin.
NZ do seem to have a few seamers knocking about who can bowl high 80s along with the usual accurate medium fast etc., whether or not they'll be effective at Test level is another matter, but they can't do any worse than Chris Martin. An unknown with potential is far better than a tried and tested old plodder.
I'll say it again Vettori is a batsman who bowls. He's better than any specialist batsman who would come in at 6/7 to take the 4th seamer's slot. So you have 6 batsmen/1 keeper/4 bowlers. Vettori's bowling is just a bonus. It's the obvious balance. You can't just play 11 batsmen because the first 5-6 are a bit average.