Hmm... it's also not quite easy to say that the song is in reference to Shakespeare, given that it's in Japanese and I don't think Shakespeare (or much English literature) would referenced a lot of in Japanese writing.

Unless anyone here is really familiar with Japanese literature, it's kinda hard to know.

There's a ton of references to Japanese myth and legend, as well as customs and stuff.
One thing I can think of offhand is in volume 4 (the episode with Satoru and Maiyu), where Souta brings Satoru a tree of folded origami paper cranes for good luck. That might be in reference to a story of a young girl named Sadakko from post-WW2 Japan. She heard that if someone folds 1000 paper cranes, they'd be granted a wish. So until the day she passed away, she continued to fold paper cranes.