IMO, I don't see any reason for the extra work nor extra storage that the additional column will require.

When the user enters two dates, SQL Server will assume that the time component is midnight (00:00:00). Instead of using BETWEEN in your queries:

WHERE datetimecol BETWEEN startdatetime AND stopdatetime

Try something like this:

WHERE (datetimecol >= startdatetime AND datetimecol < stopdatetime+1)

Pushing the ending date constraint to midnight of the next day allows the query to capture all the rows that occur on the ending day.

-Mike