Go for it!
First of all, the tensioner is a magnificent thing. It's supposed to be changed at 72,000 miles .. so if yours was done, it doesn't need to be changed until 144,000 miles.
Assume it wasn't done though.. try to change it as soon as you can.. but I certainly wouldn't be paranoid about it.
Check the part number too.. some tensioners were more expensive (hydraulic?) and your Eur350 quote may be for one of those. You have to go to an Alfa dealer and tell them your chassis number.. they will tell you what tensioner you're supposed to have, The simple spring tensioner is about Eur120 max.
The service is Euros.. but that's more or less an oil change plus new filters.. You could do that yourself and save money for changing the cam-belt.
The cam-belt is likely to be in good condition.. they last forever on the v6. Mine come out like they're new. If your belt looks dry or dusty, never mind "old" then it's the original. If it was changed 30,000 miles ago, it will look "moist" and shiny still.
Change the oil for good 10W40. Put a new filter and air filter in there.. You should also change the spark plugs...
Check the clutch and gearbox are smooth at that mileage. I'd put new oil in the box too.
That's it.. v6 is not just a normal car.. it's a legend. You will only appreciate what that means when you own it.