You can have a longer head tube on most any bike.
Yes you can but that doesn't stop the other measurements being the same. You asked 'what makes a bike ''aggressive'' ?' Generally speaking for the same amount of headset spacers and same size bearing cover, same stem length/angle. The handlebars will be lower down on a more 'aggressive' bike. Thats what i meant. The whole idea of a short headtube is to get lower and more aerodynamic.