I just did this today, and it was great. Took the north (westbound) sidewalks all the way across both rivers in both directions. There were some challenges, but nothing my hardtail MTB with hybrid tires couldn't handle; I never even put a foot down.
The easterly bridge sidewalk had some overgrown bushes impinging on it, but I just pushed through it. There were no hard branches or thorns or stickers, just leaves that gave when I pushed through. Coming up the surface sidewalk approaching the westerly bridge, I started to run into sand, large gravel, and some trash. This got worse after I got inside the rather narrow space between the railings on the bridge proper, and more vegetation impinged. For about 50 feet I would say that very skinny slick tires would have some issue; they still might make it through but one might have to walk a road bike for a minute or so. Then it cleared right up, and the majority of the sidewalk on the westerly bridge proper was nice and clear. The former stairway is still a ruin, so I exited by just riding down the ramp with traffic. It was fine and shot me right onto Doremus.
Took the industrial roads into the Ironbound: Doremus, Roanoake, Foundry, P, Roanoake, Hawkins(?) Rome. Watched soccer and drank sangria and ate great food outside at Catas on Market Street. Rode home the same way, portaged up the ruined stairway (actually rolled the bike up the flat dirt next to it). Returned to JC watching the sunset color 1 WTC orange and then red. Great day!