I need my summary to only display blank information from a Date field as a count measure.

I would suggest creating a filter that would only display rows where the date field is blank or null and then using that filter in your summary.

If you are using Data Prep Studio, you can create the named filter from the Analyze tab.  In Monarch Classic, you can create the filter from the Table Design interface.  Once the filter is created, make sure you choose that filter in your summary or export.