Potentially. Sometimes a bike commuter is someone who would've taken the bus or subway to get to work.
That said, it still depends on commuting patterns, road topography, etc. Some cities have a majority of workers driving in from distances that would be impractical for most people to bike. Making a big shift to bike lanes without making other changes to reroute and accommodate traffic would just cause gridlock and frustration for most.
If shifting city centers to being bike centric is done on a longer timeline then capital improvements and redevelopment can be done to support it in a way that makes it more efficient for everyone. Some cities can do that on a shorter timeline based on current constraints, others would take longer. Ultimately I think it's the right direction to go in.