On your unrelated A Song of Ice and Fire note, dragons would absolutely spur technological innovation in weaponry. Other countries would desperately look for a way to defend against them.

In real life, the ballistae used in the final battle were invented in ancient Greece around 400 BCE, basically about 1,500 to 2,000 years earlier than the technological level of Westeros. Bow to crossbow to ballista is a pretty logical evolution and there are intermediate links between all of them in the historical and archaeological record.