Is there any version of Checkbox that would support the creation of a Datepicker question item? If no, is there any plan to have this?
Yes, unless a system administrator has disabled the setting at the application level, you can bring up a date picker by using the open-ended single line text question. Just add that item type then, on the Behavior tab, choose one of the date formats for the Answer Format field. Then, when your respondents answer the question, they can either manually type a date or grab the calendar icon and pick a date.
Let me know if you have any other questions.