You can edit a signed PDF document (assuming you are not using the field collection feature). This will not "Invalidate" the signature, but it will change the status of the signature.
I have attached two screen shots to illustrate... To generate these, I signed a PDF, changed some data and re-validated the signature.
ValidationStatus.gif shows the status of the actual signature.
DocStatus.gif shows a "roll-up" status (meaning it checks all signatures on a doc and displays an overview) of the signed document.