I am a law school graduate. What I offer is mere information, not to be construed as forming an attorney clien relationship.
On a written agreement, if you fail to sign, but perform, yes you are bound. Performance is a replacement for a signed contract. You are essentially bound to the terms because you performed on them.
Example: you buy a car and forget to sign the financing agreement where you agree to pay 600 a month for three years. You start paying and one year into it you realize you never signed the agreement. Sorry, you are bound because you performed by paying on that unsigned written agreement.