Looks like an air return, not a supply. Cannot use that for AC supply if it is the return for your heating system.

Do you have forced air heating? If so, you would be better off adding AC to that then going the minisplit idea.

That is a far-out idea. I can say with certainty that typical high-wall unit won't work upside down because the condensed water won't drain right. There would have to be considerable modifications if it were possible at all. You might be able to put one of the units designed for short ducts in there.

Thanks for the responses! The house has an oil boiler for the baseboard radiators. We heat 95% with a wood stove though.

After I posted this I remembered a big issue with the mini splits is cleaning them, so even if it were possible it would be a huge headache with all the dirt and dust that ends up down there.

I will guess that you are in the Northeast in a primarily heating environment and no natural gas available. There may be creative ways to add a mini split unit with minimal ducting to do much better than window units. Cooling with air from the floor is not ideal. Ducts or mini splits near the ceiling is much better.