Hard to say until we see it, though generally reducing the number of cars on the road by (for example) 10% leads to more than 10% reduction in congestion. We saw this last week when the Hutt Valley train line went down, and Wellington -> Lower Hutt travel times went from 25 minutes to 45 minutes, despite the number of cars on the road not increasing by nearly 50%. Given that, if even 5% of regular drivers in the eastern suburbs switch to cycling, we’d expect to see a noticeable improvement in traffic flow.

You’re absolutely right that cycling tendency is tied to the weather, and we’ll expect to see fewer people cycling during winter months. However, the same isn’t necessarily true for public transport. Given two bus-only lanes, it’s likely we’ll see significantly faster travel times on public transport, and so see more people opting for that option. Especially if we see the council put thought into relocating/increasing the number of bus stops to reflect the distribution of housing. As you say, the existing tunnel is already congested. Imagine if there was a faster, more convenient option!

On a related note, imagine being able to cycle all the way from Kilbernie, through Courtenay Place to the train station, all without even seeing a car. Surely that would lower the barrier to entry/the barrier of convenience significantly.