Will it? Official cost analysis doesn't seem to mention oil at all, unless I'm missing something. Presumably because oil tankers are a minor part of the travel on that stretch.

Instead they estimate the value of passenger transport, tourism, increased transfer of goods transport from roads, cost savings for the fishing industry and a few others.

Investment in the oil industry is not unpopular in Norway, so they'd have no reason to keep it out of the cost analysis.

EDIT: looking at the project docs, it looks like it also won't be able to take the larger oil tanker dimensions anyway. The upper size is picked to pretty much perfectly match the largest passenger ships on the route.

It's more then oil, it's money they get for that oil....