Does SQL Server require SSLv3?
I can't confirm whether SQL Server needs SSLv3 for secure connections ... but I can tell you for sure that the MS14-066 patch introduced all sorts of problems in https traffic with reports all over the web for browsers that stopped working, SQL Server connections that all of a sudden started using high CPU and so on ... all in all a pretty buggy patch and we're all waiting on Microsoft to come clean and tell us how to safely undo it while still protecting our systems from the mystery bug that the patch supposedly fixed.

For more details see this:

http://odetodata.com/2014/11/microsoft-patch-ms14-066-leads-to-https-problems-with-iis-and-google-chrome/