만나게 될까? = Will we get to see each other? / Will I end up meeting you?
I think your understanding is basically correct. -ㄹ까? is a question ending partially directed to oneself (you could even use it to describe a question that goes on in your mind with no one around).
So the underlying meaning is probably that the two people will not meet each other in the normal sense, because they have broken up or are separated for whatever reason. But the speaker is wondering or asking the other person whether some forces in life will bring them together even though they can't or don't on their own. Another possible interpretation is that the speaker wants to see the other person and is asking whether they think they will start to see the speaker again at some point.
Simply put, 만날까? is more casual and means "Will/Shall we see each other?", while 만나게 될까? is like "Will I (ever) be meeting you at all?".