If a deal sheet is out for real estate because an offer is accepted, can it be rescinded?

I believe that a real estate deal is not a deal until all the parties have signed the contract.

The short answer to your question is NO. You can not sue.
The slightly longer answer is: New York doesn't typically utilize "Binders" (as opposed to many other States.) You did not sign a Binder. In fact, it sounds like you did not sign ANYTHING. You also did not pay anything to the Seller, which would constitute Consideration for the "agreement" you believed you had, as a result of the Deal Sheet.
Under New York State's Statute of Frauds, agreements relating to the sale of real property must be in writing signed by the parties.
You have no agreement. You had an understanding that you would try to enter into an agreement.
The deal is dead. I'm sorry you missed out. Find another apartment.
For what it's worth, while you have no legal basis to sue and have no legal claim to the apartment, MOST attorneys (myself included) will not (if for no reason other than "Karma") send out contracts to a party when contracts are already out to another party. There is nothing unethical or improper about doing it - but most real estate lawyers consider it shady/sketchy behavior.
Good luck with your apartment hunt!

Without a contract, you cannot sue.

Stephen got it right: the offer sheet/binder is not a binding offer in and of itself, and the statute of frauds requires a written contract for sales of real estate. The real-estate business is a ruthless game, and people often get left at the altar even AFTER signing a contract. Therefore, fret not, tighten your belt, and onward!

The statute of frauds requires that a contract for the transfer of real property be executed by the party to be charged. It does not have to be signed by all parties. That is, if you, the buyer, are seeking to enforce a contract against the seller for the transfer of real property, the contract must be signed by the seller.
It is possible that a "deal sheet" could constitute a contract if it is signed by the seller and contains the terms necessary for the transaction. That being said, if you have no written contract (binder, deal sheet, or otherwise) executed by the seller, you are likely out of luck.

Without a contract, you cannot sue.