First, your employer will normally ask you for your signature to only acknowledge that you received the document; not that you agree with its contents, so there is really now downside to signing it.
Secondly, an employer can lawfully terminate any at-will employee for refusing to sign that type of document, referring to it as insubordination. In the absence of significant evidence that the true reason for termination is discriminatory or retaliatory, this would not be a wrongful termination under the law.
Lastly, being terminated for refusing to sign any type of warning or PIP is particularly costly if you are terminated right before a portion of your RSU vests or your bonus is earned. In this case, you may be losing a significant amount of money for no good reason.
I can't think of any good reason to refuse to sign a disciplinary notice. It can't make your situation at work better, but it can make it worse by ending your employment and/or also hurting your earnings that you would otherwise could have received.