Nope. You need a LOT more involved stuff than that to make that conditioned living space.

It may be possible if you can add insulation to the sofit. If you don't you will get a large cooling loss.

Sunrooms and bonus rooms over garages tend to heat up more quickly and cool down more quickly than other living areas. Even if you can add to your existing duct system, I don't think it will be comfortable without zoning--which may not be feasible. I think you'll be well served to install a dedicated unit (e.g., mini-split) in the room.