As you already suppose, the angle does make a difference.
To your first question: If you take the distance between the wheel axles as a constant measure, the handle bar will get further away from the saddle the higher the head tube angle gets, therefore the geometry gets "longer". This can for a certain amount be compensated by a shorter stem.
The bigger effect is - you guessed it - on the steering behaviour. A flat head tube causes the steering to get more stable, so its tendency to go straight is higher. This means that if you compare a bike with a flat head tube to one with a steep one, the flat one will feel like driving on rails, meaning you feel like you have to "force" it into curves as it tends to go on straight.
The most interesting question is if the difference of half a degree really would make a difference but I think it won't. I can remember that when I bought my last bike some time ago that the different bikes that made it to the final decision had some spread over some 1 or 2 degrees in head tube angle, but they were all from the same price and purpose class. So I would say that such a small difference will be more due to technical decisions of the manufacturer than due to better or different handling.