I have my doubts, shall we say.
Let me tell you about the town my dad grew up in. It used to be bustling, lively. The economy was based around factories. There was lots of money going around. If you wanted a decent wage, you could work at a factory and make that money. The last factory to leave was a soda bottling plant. Now there's nothing that generates money there. The only way out is to make grades good enough for college scholarships or join the military. But old people still stay there. People without the ambition to go to college or join the military still stay there. So, now it's a town filled with nothing that generates any money, old people, and unambitious people. Predictably, the previously bustling downtown is gone. The only businesses left are a liquor store, a fast food restaurant, a dollar store, a small grocery store, a barber shop, and a few antique shops with no employees just owned by old people with nothing else to do. The only money in the economy is generated by old peoples' savings and welfare.
The richest guy with the biggest ball swinging job in town is the cashier at the dollar store, rolling in just a bit more money than the guys on welfare.
The only way that place could support a $15/ minimum wage without losing the few businesses it does have left would be more welfare payments pumping money into the economy. $15/ hour without more welfare would make the town even more depressing. Then the town would just be old people that are too poor to move out surrounded by unemployed drug addicts that used to work at the dollar store, and no place to buy groceries unless they drive an hour away (which they already have to do just to buy clothes or see a movie).
Honestly these places shouldn't exist anymore. I don't want to pump even more welfare into them to just keep them barely stringing along like zombies. They should just be allowed to disappear and become abandoned relics of the past.
HUGE parts of the US are exactly the same. Their economic generating activities are completely hollowed out by industry leaving the US and being shipped off to developing countries.