Good question.
I am not well-versed in the eSATA as yet, and therefore I failed to make an important distinction earlier-- eSATA drives require external power, whereas eSATAp provides power for that type device. There is 5vdc available, it seems, through the USB interface (eSATAp sockets can also be used as traditional USB ports), and 12vdc available, at least on desktop computers, for running larger drives (3.5" drives and opticals). It seems, though I have not been able to verify this, that the 5vdc power used for 2.5" notebook drives comes from the Southbridge.
That is, the Southbridge portion of your computer's chipset provides the USB and other peripheral interface (hardware) drivers, and while those drivers do provide 5vdc for the USB interface to power devices plugged into it, some of those Southbridges (in the past, at least) were susceptible to damage from heavy loads placed on them.
This is why I and many other hardware gurus recommend that you use an externally-powered USB hub between your computer and any USB devices which draw more than a minimal amount of current and/or if you have a habit of adding and removing USB devices on a regular basis with the machine powered on.
In the case of an NAS drive, then you would probably want to have an external power source for it anyway, regardless of the interface.