During enumeration, the EDBG reports a current consumption of 500mA, and must therefore be connected to a USB host that is capable of supplying this. It is impossible to predict the amount of current required by the setup, since the EDBG is a part of a flexible evaluation kit.
The EDBG alone consumes approximately 100mA during usage. When the EDBG does not detect a VBUS voltage, but is otherwise powered (for example through the Xplained Pro PWR header), the EDBG will go into sleep to minimize power consumption. The power consumption during sleep mode will vary with the design, but should be well below 1mA.