Sure, it is. This book has the elements typically found in literary fiction like deep exploration of human emotions, sophisticated language, and a focus on character development.
I'm sorry, I don't know the author of this 'tomorrow and tomorrow and tomorrow a novel' as the title is not very common in my knowledge. You could try searching for it in a library database or a good book search engine.
The 'tomorrow and tomorrow and tomorrow short story' might have a theme related to hope or the lack thereof. If it focuses on multiple 'tomorrows', it could be showing how characters either look forward to the future with anticipation or are trapped in a cycle where each new day (tomorrow) is just like the last. Without reading it, it's hard to say for sure, but these are some common interpretations in literature related to the idea of successive days.
Another theme is exploring the backstories of the characters more deeply. In the actual drama, there may not have been enough time to fully develop all the characters' pasts. Fanfictions can fill in those gaps, like delving into the character's family history or how they came to be the person they are in the drama.