Is anti virus a battery hog?
Yes, AV is a battery hog.

You are looking at three different processes, actually. The first is SophosServiceManager, which looks like the process that is actually doing the scan.  It looks like it's taking tons of CPU (and thus battery).

SophosUIServer probably just displays the little icon in the menu bar, and takes almost no memory.

SophosScanD is yet a third process.