...what would have happened?
Well, as we engineers try to teach plumbers with limited success, "Friday's payday and (sewage) don't run uphill". If the idea was to flood lower Manhattan, it ain't gonna happen anywhere above sea level. Long term, anyway.
But unless you're a Democrat and/or you work for the Congressional Budget Office, you can't ignore dynamic effects. Let that water go whooshing through that tunnel and it will have a lot of momentum by the time it emerges at the ends. I.e. you'll have a mini-tsumami of sorts, which will wash away a lot of stuff and anyone unfortunate enough to be standing or driving around. Of course this depends on how big a hole you have and how suddenly it materializes, but the idea is that there are more ways to make messes than just flooding.
And while there might not be lasting flooding above the level of the Hudson, there are plenty of things in Manhattan that are built below grade. If you want to know what happens when these flood, just ask a Chicagoan. And if you think there aren't tunnels like this under Manhattan, guess again - here's just one example.
The irreplaceable Kate at Small Dead Animals points us to this, which goes into more related topics.