No the amount of traffic remains the same. Offering alternatives to driving reduces it. More roads = more cars is a fairly well established fact:
How Does Roadway Expansion Cause More Traffic? | Blog | Science Museum of Virginia.
I'm still not sure you get it, if you decrease the infrastructure and cause a bottleneck. It causes more traffic.
The only way it will reduce it is if everybody suddenly decides to use a bike and again, it's not really viable for a lot of people.
If the council and whoever want more people in the city centre then they have to decide how they want them to get there. If they want everybody on bikes, fine. What are those people going to do in town once they arrive on their bike? Where are they going to put it so that it isn't stolen?
If there was better public transport, people could leave their cars at home. They aren't all going to suddenly get a bike.