It depends on their design, but if one fails the other fully takes over the load. It is (or at least should be) totally transparent to you. No reboot/glitches should occur. In a typical data center situation there's some type of monitoring software installed so you're notified when this occurs (email, text, or page).
It's easy to test. Just unplug one of the power cords.

You can further protect uptime by running each power cord to a different UPS. That way if a UPS fails your systems still stay up.