While the date auto populates you can enter any date you like. If you are going to enter your own date it really does not matter if there is a date there or not does it.

 Are you manually entering an AP invoice or creating one with a script?

Thanks BigLouie. You‘re right I can enter the date any time. However our users sometimes neglect to enter the actual invoice date when there is a module date has been auto populated. So we would like to have this field blank when an invoice created in order to make sure user to enter actual date. I'm not creating AP invoice by script.    

I'd try two scripts on the header table.  First, set default values trigger, to make the date something like Jan 1, 1900.  Then a second script, pre-write, to set error whenever encountering that date.