I think that is one interpretation of this story: that it depicts a modern society that mocks individuality. The big guy is the individual and the narrator feels sympathy for him but doesn't really understand him. The narrator even feels that the big guy is more dangerous than the other wise guys at the station who are much more aggressive. So, there is some irony there: individuality is seen as more dangerous than aggressive behavior itself.
But the story is also about experience. The big guy repeats "drowning" as if to imply he could drown in the vastness of Brooklyn - in which case he's agreeing with the narrator that one can never know all of Brooklyn. The big guy wants to experience it all. The fact that the narrator and the wise guys are arguing over how to get around underscores the vastness of Brooklyn. Analogous to that idea of "many roads" is the figurative idea of many ways to experience. The narrator is curious about the big guy's curiosity; maybe he's curious as to why the big guy chooses to wander everywhere as opposed to experiencing nuances of some of Brooklyn.
When the big guy asks the narrator if he would save a drowning man (big guy can't swim and will get lost - drown - in Brooklyn w/wo the map), I think he's asking in order to find out if there are others like the narrator who'll help him out if he needs it. In this case, the big guy gets confirmation that although he's different, others (wise guys or whoever) will help him out. This goes against the idea that it is a society that ONLY ridicules individuality.
The narrator must know that one of the reasons 'one can't know Brooklyn in a lifetime,' is the vastness of it, the variety of culture and with that, the variety of individuals.