There was already some amount of cultural awareness about the Titanic prior to the movie, after all they pretty much started making movies, plays, documentaries, etc. as soon as it happened and kept right on making them

It also got a pretty good bump in popularity when the wreck was found in the 80s

Even if the movie weren’t made, there’d probably be a pretty decent chunk of people who would know about it from the scene in Ghostbusters 2 if nothing else.

It probably wouldn’t be something that pretty much everyone knows about, and certainly not in the kind of detail we do now, but you’d probably still have a pretty good chance of people who’d at least know that it was a big passenger ship that sank.

It’s hard for me to be impartial about this though, I was in elementary school when the movie came out, prime age to learn how to play “my heart will go on” on the recorder in music class and to see that big brick of 2 VHS tapes for rent in blockbuster. To this day I actually haven’t seen it, but it’s hard for me to imagine a world that people don’t know about the Titanic because the movie was just so omnipresent in my formative years.