Yes. Both US and European law have long recognised that electronic signatures are admissible in legal proceedings to determine the authenticity of any electronic communication in which they are incorporated.
Although a signature is commonly regarded as the writing by hand of one’s full name or initials and surname to confirm one’s willingness to be legally bound by a set of agreed terms, the courts have recognised that the essential characteristic of a signature is not what it looks like but the purpose it serves. That is, a signature must demonstrate a signatory’s authenticating intention (that the signatory intended to be bound by the terms of the document).
A person putting their thumb print on a document could be valid as a signature as it would be evidence that the person intended to be bound by that document.