Android phone HDD/SSD 2.5"/1.8" - how much power is too much?
USB flash drives consume about 1-2 watts, SSDs max 5 watts and good HDDs 6.5-7 watts. I doubt a low powered USB connection could power an HDD. Perhaps a portable HDD since those use a bit less power.

Sources: 
http://www.buildcomputers.net/power-consumption-of-pc-components.html

http://techreport.com/review/25391/wd-red-4tb-hard-drive-reviewed/3

https://superuser.com/questions/565653/how-much-power-does-a-hard-drive-use

http://www.anandtech.com/show/8747/samsung-ssd-850-evo-review/10

https://en.wikipedia.org/wiki/USB#Power

http://www.anandtech.com/show/10163/usb-flash-drives-power-consumption-measurement-using-plugables-usbctkey