Nice work, Peter! Thanks for posting this up.
Couple of suggestions...you might be able to cut the reads down on the ros table using something like this:
;WITH ros AS (
 SELECT VolunteerID,
  DateFrom = Cast(ROS.DateFrom As Date),
  DateTo =  Cast(IsNull(ROS.DateTo , GetDate()) As Date)
 FROM dbo.RecordOfService
)
SELECT
 t.VolunteerID,
    [FromWhen] = CONVERT(nvarchar(12), t.FromWhen, 105),
    [ToWhen] = CONVERT(nvarchar(12), t.ToWhen, 105),
    t.NoOfWorkingDays,
    [VirtualEndDate] = DATEADD(D, t.NoOfWorkingDays - 1, t.FromWhen),
    [DateDiffAsYMD] = dbo.fnDateDiffsYMD(t.FromWhen, DATEADD(D, t.NoOfWorkingDays - 1, t.FromWhen))
FROM (
 SELECT
  ros.VolunteerID,
  [NoOfWorkingDays] = COUNT(DISTINCT d.[Date]),
  [FromWhen] = MIN(ros.DateFrom),
  [ToWhen] = MAX(ros.DateTo)
 FROM dbo.DimDate d
 INNER JOIN ros
  ON d.[Date] BETWEEN ros.DateFrom AND ros.DateTo
 GROUP BY ros.VolunteerID
) t

Secondly, that UDF will inhibit parallelism - I wonder if it can be converted to an inline table-valued function...