From a macro perspective, if this stadium isn't going to draw people from outside the city that would be spending their money somewhere else doing something else, then you're probably not going to infuse much into the economy. You'll get that some initial surge if local workers are hired who would otherwise be out of work to do the development, but after that it would go back to the status quo.
However, if this stadium offers the opportunity to host A list concerts that seat 30-40k, major sporting events outside of SU sports (i.e. boxing) that can have large draws that the area can't currently support, then you may be on to something.
The key is new revenue generating opportunities that don't cannibalize current revenue generating opportunities. Because then yes, you're basically spending $200M or more to move Joe's Pizza crosstown into a nice shiny new building that is still going to draw the same number of people spending the same dollars that they would have otherwise.