SharePoint list date types are different from InfoPath. And, I'm pretty sure they are not XML date types. In other words, they don't have xsi:nil attribute.
You can't use out-of-box 2010 ShP list/library filters to find blank values, but you could have your list automatically set them to some dummy value (like "nodata") and you could filter on that.
Another option is to use the REST listdata.svc which will support complex filters like &$filter=date eq ''
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