Top tubes can be longer, shorter, or equal in length to the seat tube. If that top tube is the right length for you then it may be possible to make that frame work.

I'm no fit expert. There may be some fit issues caused by raising the seat up so high because as the seat goes up it moves back away from the bars and away from the BB.

A good place to start with a road bike is with the bar height and seat height pretty much level, and like you said, it would take a taller stem to get there. The longer stem will push the bars back toward the seat a bit, and you may end up wanting a longer reach stem than you have now. It's kind of a cascade of adjustments.

The best bet with this bike may be to get an adjustable angle stem with a 2 bolt clamp. Then you can tweak it to figure out the (close to) ideal stem position. After that get the appropriate sized stem, hopefully with a 2 bolt clamp so you don't have to untape to install it.

Last thing - adjust the seat so it's level with the ground. Looks like the nose may be tilted down.