I have been in contact with the MTA and this was their response:
"We don't accommodate ceremonies of any kind within the general public areas of the terminal. But I recommend you reach out to Cipriani Dolce and see if they can accommodate your quick ceremony within their space, which overlooks the Main Concourse. If you decide to proceed with the restaurant and want to take wedding photos afterwards in the general public areas, the photo permit is something I can assist you with.
Permits are issued for up to a 3-hr time slot, no more than two months and no less than a week in advance of the requested date, on a first-come-first-served basis. In order to avoid the rush hours, on week days you are limited to a time between 10 AM and 3 PM (10 AM and 1 PM on Fridays in the summer) or after 8 PM. Weekends have no official rush, so time is more flexible. Please note as this is an active train terminal, there are black-out periods where no permits can be issued. Note, you will not be allowed on any staircases, landings, or anywhere beyond the train gates."
You can rent out the terminal entrance, Vanderbilt Hall, for all types of events, just not weddings. Cipriani Dolce won't accommodate weddings with more than ten guests. And the Grand Central Oyster Bar is a little rich for our budget, at $127 per person for a buffet style meal.