It's possible to take damage and enter a cutscene at the same time. This causes some strange behavior depending on what cutscene you died in, with some cutscenes having visual glitches and others skipping text outright. Despite skipping some text, this usually is not faster as Link will lose all his items and be sent back to Ravio's Shop.
NOTE: Using a fairy to revive yourself in a cutscene trigger cancels the glitch and the scene plays normally.