The group that the Missionary in Point Lookout was from 'The Faith'. She is located in the South-West portion of the map, where the four tents are. She even says she is from the Faith. I just re-played Point Lookout, I would know.
But why would you assume that this The Faith has a presence in the Commonwealth?
I think that the game can have New York in it, New York is right next to Massachusetts. Much like Fallout 3 having Virginia in the mix of it.
If Bethesda plans on doing a single wasteland like they did with Fallout 3, and also plan on including The Institute, which is near Boston, then no, they can't have New York in it, as Boston is quite far from any part of New York.
Well, if the player would successfully escape the Institution, there would be Synth Retention Bureau Security that is looking throughout the Commonwealth Wasteland trying to find the Player Character. But your idea is good, too.
The Institute is a "sealed environment," so says Zimmer, so I really don't think escaping is viable. And there is no Synth Retention Bureau "security," because they
are security, or rather, a "special branch of the Commonwealth Police." Yes, the Commonwealth has a government and a police force with it's own sub-branches, it isn't like escaping a single faction, you're escaping an entire government.