I think it would depend on what you're defining as 'that city.' If you mean the legal entity that enjoys tax revenues then yes, but for the people already living there they won't be getting those $100,000 Amazon jobs. So that means a bunch of people from outside the area suddenly moving in with a lot of money to throw around.
Sure, there will also be network effects where service level jobs expand but having been priced out of their former neighborhoods, watching people with perhaps little respect for the local culture or history coming in and changing things, I don't think the prospect of Amazon's new HQ is really all that positive for a city struggling as you hypothesize.
It doesn't help the people currently there at all. The only people begging for it to come are those who can already afford to live in a place where rents are through the roof.
In Austin Texas, the historical legacy of racial segregation meant that there have been areas of the city that were predominantly hispanic or black, for generations. The modest homes in these neighborhoods were paid off long ago and passed down through the families.
When the development boom hit Austin, even the parts of these neighborhoods that didn't undergo gentrification have seen a massive pressure on the folks who did live there in the form of explosive property taxes.
For many of these folks, this has pushed them out from their family homes because they can no longer afford the taxes on their properties, despite owning them outright. Of course there is an argument to be had about why these folks can't afford the taxes but heavily under-girding that is the same neglect and marginalization their populations have always faced.
So even owning property is not always enough to insulate someone from the whims of explosive development aimed at those with extremely large incomes.
Sure it does. It benefits homeowners and businesses, and anyone who benefits from a broader tax base.
It DOESN'T help people who are on the margins, though, unless they can get a job at the new employer, or unless public services improve more quickly than housing costs go up.
It's called NIMBY.
Related reading: "..cries of Not In My Backyard are quietly costing the United States economy trillions. " => https://www.forbes.com/sites/christopherhelman/2015/07/30/ni...