How do I drop the TIME portion from DATEADD?
Well, assuming that someone is holding a gun to your head, forcing you to not change the data type to something more sensible and logical:

UPDATE CCCINC.dbo.Employees
SET DateOfBirth = CONVERT(CHAR(8), DATEADD(DAY, ABS(CHECKSUM(NEWID()) 
  % 41975), '1900-01-01'), 112);


Strong, strongly, strongly suggest you change the data type of that column to use the right data type (DATE). Then you can just use your original query and not worry about the "format" at all. Format is what you worry about when you present the data, not when you store it.


Bad habits to kick : choosing the wrong data type
Bad habits to kick : mis-handling date / range queries