The click of the button cannot cause a signature to happen. The user will have to click on the signature field for that, but you can validate whether the signature is there or not and cancel the submission if it is not.
I would hide the submit button and use a regular button (that way I can script behind it). The code should check to see if a signature is present, then lock all fields (if you didn't do it through the signature), then press the submit button. If the signature is not present then put a message up telling the user they must sign the form first.
There was a post recently that showed how to check for a signature, you may have to search for it.