Will my Cinema HD Display work with a new Mac Pro Quad Core?

Yes, if it uses a ThunderBolt or Mini DisplayPort, it plugs in directly.

If it uses a DVI:

Can I connect DVI displays?

You can use two DVI displays with your Mac Pro. If you connect a third display via HDMI, it will cause one of the three displays to become inactive. To avoid this, consider using Thunderbolt, Mini DisplayPort, or VGA for connecting additional displays if you are already using two DVI displays.

from:

Mac Pro (late 2013): Using multiple displays

.

Yes.

Thunderbolt ports and displays: Frequently asked questions (FAQ)

https://www.apple.com/thunderbolt/

http://support.apple.com/kb/HT5299