This sort of mechanistic view, that the Renaissance is Thing B brought about by Thing A, both with clear temporal, geographic and conceptual boundaries, is not the right way to go about this. A Medievalist, for example, could rightly object to this narrative that the barbarous west needed to be "Enlightened" by the civilized east. An Italian historian might object to the way the specifically Italian context is being ignored. An art historian might object to Brunelleschi and Alberti being chronologically shut out. A classicist (cough) would probably object to the way this ignores that the humanists were primarily concerned with Latin material, such as Cicero.

So there are a lot of angles to attack this narrative.

That being said, the Byzantine Empire was pretty obviously in a bad way well before 1453. Its bacon, for example, had been saved in 1402 when Tamerlane crushed the army of the Sultan Bayezid, who was at the time conducting a siege against Constantinople and was one of the most impressive military leaders of his day (and who happened to have the misfortune of proving the adage that there is always a bigger fish). So the Byzantine Empire was pretty desperate for assistance, including an attempt in 1439 to end the Great Schism. As part of this, many notable intellectuals traveled west as ambassadors, cultural and political. One of them, Manuel Chrysoloras, taught a young Florentine how to read Greek--the young Florentine being Leonardo Bruni.

So there was definitely a bit of causality there.