If they are running SQL Server in case insensitive mode (the default), this will be an expensive operation as you'd need to post filter any of the results you get from SQL Server to do the case matching. This would increase the processing required on the web servers, though it's really unclear how much since we don't have any idea how often it would be used. I was going to suggest using Google advanced search against site:stackoverflow.com, but they apparently have omitted case sensitive search from their tools. Perhaps they know something we don't. ;-)
Some basic facts (from Google help)
Every word matters. Generally, all the words you put in the query will be used. There are some exceptions.
Search is always case insensitive. Searching for [ new york times ] is the same as searching for [ New York Times ].
With some exceptions, punctuation is ignored (that is, you can't search for @#$%^&*()=+\ and other special characters).