Yes and no. From my experience so far (currently about 16 hours into the game at Honeybee Inn story arc), it's more that it's "expanded upon" rather than anything new. Most of the new things fit so well with the story that you feel like you just forgot about it rather than you experiencing anything new.
They did a really good job, and I mean really fucking good job at keeping true to the original with new content. With that said, at least so far, there hasn't been anything that I would classify as a spoiler yet for anyone that has played the original. There is a lot of foreshadowing later events (llike Aerith dying) that I don't remember being hinted at this early in the game before.