I think you can safely use the clinical events with missing dates as exclusion criteria only. As in “exclude any and all persons with X at any time”. With X being the clinical event missing the date.
If you believe your data are accurate and the clinical event which lacks a date really did happen, then you could put these data into the Observation table with other “medical history” data. The date of the Observation record is the date the data were recorded. So, this would be the date of the ETL. The observation_concept_id = 1340204, History of event. And the observation.value_as_concept_id is the clinical event which lacks the date. Make sure you document all these decisions in an easily readable specification document, so the end users know you included these data and where and how to find them