No, not unless you husband informs USCIS. However, if the divorce becomes final before your I-485 is granted, you are no longer entitled to a green card. And remember, you will later have to file an I-751 petition before your two-year green card expires.
It's clear under the law that if you divorce before the I-485 interview or before the granting of the lawful permanent status, you would not be able to continue. However, your question was not detailed enough. For example if your husband abused you, you wold be entitle to obtain the Green Card without your husband's consent, under the battered spouse provisions (VAWA)