This connectivity really only speaks to car and bike connectivity. The success of 3rd St. as a gathering place for the area should be separate from its connectivity, that could actually make it easier to just turn vehicle traffic away from it. The ground-level CRUs of the adjacent properties to 3rd is pretty bad. Only 3rd St. between 4th and 5th Ave is anything close to what you would want.
What scares me is we talk about 'improving the street scape and that should help make the CBD better', 3rd St has a fine street scape, its the closest thing to a complete street and yet its an awful street. It could simply be because of the poorly integrated CRUs. If so, take that residential conversion money, put it into those CRUs and you might make it better but really I don't even have faith that would make it better. Take a drive down 3rd and the large flower beds and other elements put in to make it a 'friendly street' really have the opposite affect and break it up and make the street feel very gray and brown, even in the summer.
3rd St. does have a lot going for it though and you could even keep the stale connectivity to the ground-level of buildings... Jack hammer all of that cold concrete and brick, make one pedestrian walkway right up the middle with minimal concrete, plant some native plant species, grasses or whatever (I'm not a landscape architect). Where there are ground-level CRUs integrate them into the urban garden where there aren't run the vegetation right up to the building and in a sense hide the lack of CRUs. Create some small-scale plazas for food trucks and other events and you've given people a reason to go there. Then all you have to do is properly connect it through to Eau Claire and The Prince's island park and you've got yourself a green street. Give the Sheraton access to their lobby via a one-way loop and I'm sure they'd be happy to be located along a green street.