If the event has no date, I won’t know whether or not to show it somewhere, nor when. So it is simply not possible. My suggestion “Just use a startdate in the past and an end date in the future and make sure you show ongoing events” works ok. If you conditionally don’t want to show the start or end date for a specific event, a simple method would be to add a category to it and using [eme_if] to test for that category and only show the info when it doesn’t match.
E.g.: [eme_if tag="#_EVENTCATEGORIES" incsv="mycategory"] show stuff like #_EVENTNAME [/eme_if]
The thing is here that you’d also need a “notincsv” variant, so that for those not matching your category you can show the date/time … That will be in the next version, for now you can also use
[eme_if tag="#_EVENTCATEGORIES" contains="mycategory"] show stuff like #_EVENTNAME [/eme_if]
[eme_if tag="#_EVENTCATEGORIES" notcontains="mycategory"] show stuff like #_EVENTNAME and #_STARTDATE #_STARTTIME[/eme_if]