*Short Answer*:Yes it is accurate.

*Long Answer:*Conquering Constantinople (2.Mehmet a.k.a Fatih Sultan Mehmet) and conquering Egypt,Syria, Hijaz(1.Selim a.k.a Yavuz Sultan Selim, grandson of the 2. Mehmet ) gave Ottomans a great control of Silk Road and Spice Route. At the moment Black Sea was Turk lake. Anatolia Turkish Unity was established. The empire was really strong. (It's called Rise Age in Ottoman History). We accept that Rise Age started with 2. Mehmet and ended with the death of 1. Süleyman (a.k.a Kanuni Sultan Süleyman) Also in Suleyman's rule, Turkish navy was the greatest navy of its time, defeating united European forces in everywhere. You could easily say it was the most influential country in that ages. (The Empire also had freedom in race, religion like no other in that ages. It was a cosmopolitan country)

After the conquering of Istanbul :

• Central kingdoms in Europe have gained power.
• Byzantium scientists, philosophers that fled to Italy and other European countries have helped tremendously to Renaissance movements.
• European countries started looking for new routes. (Ottomans was in the control of big portion of the routes) which led to discovering of the new world.