POE for GS305P

Can the GS305P switch be powered for its own internal functions by its LAN connection to a POE network switch?  I need to split an ethernet connection to two to four desktop PC's, and have a client insisting on a ceiling-mounted data cable reel.  There will not be any free outlets to plug in the switch.  They are all being used by the actual PC's, montitors, etc.

 I'm trying to avoid installing a separate reel for each data connection.