Can it be set up so a password is required to insert a saved signature - for a signature as an image/saved signature from Fill and Sign menu, not a digital adobe id signature.
Sorry for the delay in response to your query and apologize for the inconvenience caused. The Adobe Fill and Sign does not offer to protect your Signature as an Image/Saved signature by a password.
You can use Digital Signatures as they are password protected, for more information, you may refer to Digital IDs in Acrobat
You may also refer to About certificate signatures in Adobe Acrobat
Feel free to update this discussion in case you need further assistance.