Are Seagate Constellation or Enterprise V.3 drives compatible with MiniPro enlcosures?

No. Seagate Constellation 2.5" inch drives require both 5V power from USB and an additional 12V from external power. The MiniPro will not supply enough power to the drive, even if the MiniPro's 5V external power supply is utilized.

UPDATE (10/5/16): Seagate has re-branded the Constellation drives as "Enterprise V.3". These drives still require 12V of power and will therefore not power in MiniPro Enclosures.

Head to this link for more information on the MiniPro's powering behavior.