Yes, no problem. Just set TimeRangeSelectedHandling to "PostBack" or "JavaScript" and handle TimeRangeSelected/TimeRangeSelectedJavaScript event to be notified about the new date selection.
You can also use it as a date picker (it's wrapped as a <DayPilot:DayPilotDatePicker> control). A date picker demo can be found here:
https://www.daypilot.org/demo/Calendar/DatePicker.aspx