Currently no, all-day events are not directly supported on the calendar. However there are workarounds. The basic workaround is to create Datetime Formula Fields, or Datetime fields that are populated by a trigger or Workflow Rule, that calculate a Start Datetime and End Datetime based on the all-day Date field. This strategy can be applied to pretty much any object, and generally works pretty well.
With the Salesforce Event object, unfortunately, neither StartDateTime, EndDatetime, or ActivityDate are available in Formula Fields or Workflow Field Updates, so you'll have to create a Trigger if you want to auto-populate custom Datetime fields based on these fields. If you'd like we can share some sample trigger code to help with this.