Technically there is no agreement until the landlord also agrees (usually indicated by the landlord's signature, or in this case the management company), but in essence you have indicated your commitment to agree by signing the document already. It's a little bit of a grey area but generally no, you cannot backout unless the landlord mutually agrees. You will still need to give your landlord notice of your intent to terminate the tenancy ("move out notice") with whatever minimum time is required under NY law, even if your current lease is already expired at that point.

