Thanks, I took a look at that. I couldn't make that solution work for me because there are four submit buttons in my form, as it passes through several reviewers. So what I had to do is enter the code below into the Click event for each section's Submit button, so that it at least gives a reminder to sign before submitting. It doesn't stop the e-mail from popping up, though, unfortunately.
var oState = event.target.getField("form1[0].Page4[0].DeptReview[0].EA_Signature[0]").signatureValidate()
if (oState == 0)
{
xfa.host.messageBox("You have not signed the form. \n\nPlease click OK and then click the signature field to sign the form. \n\nThank you!");
}