Amtrak is already proceeding on a new tunnel project under the Hudson[0] independent of the Gateway project, (edit: and has funding independent of the federal government). The real question is if elected officials can get on the same page with the interstate Gateway project.
It is still owned by Amtrak, which means that normal commuters will still get the short end of the stick over Amtrak customers like normal. Any one that takes NJTransit during rush hour knows just how little Amtrak cares about commuters. For those who don't. They on a regular basis posted track numbers for two rush hour trains leaving within 5 mins on the same track pair. This leaves more than 300 people rushing down the same 3 stairwells.
[0]: https://nec.amtrak.com/project/the-hudson-tunnel-project/