As a former realtor in the NYC area, the answer is NO! The reply from Alan is wrong. The reason is if you did NOT sign a broker agreement, the agent will need proof in writing that you owe a commission. Since the agent has no written proof (no signature from you), how can the agent prove in court that you owe anything? Any agent can say they showed you a rental apartment, but it will be your word against theirs. In court, anything verbal is thrown out and a judge will want something in writing.
You scored big on this one - Congrats! If this were outside NYC, it would be nice to pay the agent a commission since there are fewer agents and less population. But in NYC, you can easily get away without paying. Most agents in NYC collect the brokers fee upfront BEFORE they show you any rentals. This way they already have your signature.